Non-probability sampling is defined as a sampling technique in which the researcher selects samples based on the subjective judgment of the researcher rather than random selection. Multivariate Probability Distributions. However, to cement your learning, and see theory in practice, nothing beats some good ol’ fashioned examples. Lecture 3: Continuous distributions, expected value & mean, variance, the normal distribution 8 October 2007 In this lecture we’ll learn the following: 1. 0—its derived counterpart, the probability of failure, or P f, are the expressions required to calculate the expected value of an exploratory drilling venture. Borel-Cantelli Lemmas 4. And here, first of all, we'll look at the laws of probability and do some examples. There are two outcomes (win and loss), each with its own probability. Arenas, published on September 24, 2019. Linearity of expectation is the property that the expected value of the sum of random variables is equal to the sum of their individual expected values, regardless of whether they are independent. 1 0 0 X 1 0. 67 days (rounded). Since you roll 3 dice and there seems to be a probability 1=2 that your chosen number appears and so the odds should be in your favor. Probability Distributions & expected values 2. Use These Examples of Probability To Guide You Through Calculating the Probability of Simple Events. Predicted Probability from Logistic Regression Output1 It is possible to use the output from Logistic regression, and means of variables, to calculate the predicted probability of different subgroups in your analysis falling into a category. For example, we can see from the plot that there is only one value of 94, and three values of 89. Just as we did in the previous two examples, we multiply the probability of success by the number of trials to get the expected number of successes. The probability fractions are statements about the proportion of outcomes from an activity that can be expected to occur in many trials of that activity. How to use expectation in a sentence. Distributions 3. We refer to this random variable as the conditional probability that X • a given Y or as the conditional expectation of ga(X) given Y. Conditions for a valid probability density function: Let X be the continuous random variable with a density function f (x). If each hunter independently hits his target with probability p, compute the expected number of ducks that escape unhurt when a ﬂock of size 10. Example 8 Here we use so that there is a still a long right tail but 90% of the weight is on the other side. EXAMPLE 3 Using the Hypergeometric Probability Distribution Problem: The hypergeometric probability distribution is used in acceptance sam-pling. The total for that node of the tree is the total of these values. A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence. g Probability of getting even number in rolling a fair dice is 1/2 which is same as probability of getting odd number but the expectation of getting even number is 2 which is not same as 1. expected value = probability of wining × payoff - probability of losing × bet amount. The expected, or predicted, numbers for this case of 50 percent probability with 30 trials are 30(. Probability: Theory and Examples. A simple example illustrates this law. When asked to find the probability of A and B, we want to find out the probability of events A and B happening. identical to pages 31-32 of Unit 2, Introduction to Probability. 5 as the number of rolls approaches infinity (see § Examples for details). Rather, it is an expression of the scholar’s subjective be-lief. chosen appear on the the three dice. The conditional probability of coughing by the unwell might be 75%, then: P(Cough) = 5%; P(Cough | Sick) = 75% The concept of conditional probability is one of the most fundamental and one of the most important in probability theory. For example, imagine a six-sided dreidel where the two additional sides say S, where you lose one. We can now set up the expected value equation. So the expected value equals (0. DIST, in which case the Chi square of the random sample must then be passed as a parameter instead of the data row. Beginning with a concrete example, let n= 8, and the outcome success, fail, fail, success, fail, fail, success, fail. 3, random variable, expected value. Deﬁne µ(A) = #A. In the example in figure 2, the value for "new product, thorough development" is:. Excel document collects class’ data to compare to individual results. So we can now calculate the condition expectation, which, in this particular example, would be 1/3. by Marco Taboga, PhD. Expected value. The probability that Y takes on some value in a set A can be expressed as an expectation using the indicator function: P(Y 2A)=E(IfAg(Y)) (3) where IfAg(Y) is the indicator function that takes the value 1 when Y 2Aand 0 when Y 62A. Site: http. For example, we may say that it will probably rain today because most of the days we have observed were rainy days. Last Updated on November 1, 2019 Maximum likelihood estimation is an approach to density estimation for a dataset by searching across probability distributions and their parameters. So, firstly, the laws of probability, definition that probability is the relative likelihood that a particular event will occur. For example, the length of time a person waits in line at a checkout counter or the life span of a light bulb. It is the ratio of the number of ways an event can occur to the number of possible outcomes. 1 0 0 X 1 0. If two random events are independent of one another, the probability that both will occur is the product of the probabilities of the individual events. Probability, Expected Payoffs and Expected Utility • In thinking about mixed strategies, we will need to make use of probabilities. If we then add all these up we obtain the expectation of X. b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. You want to calculate the probability (Poisson Probability) of a given number of occurrences of an event (e. In particular E(X2jY) is obtained when g(X)=X2 and. It can be interpreted as the long-run average of many independent samples from the given distribution. I'm in the middle of exams right now so I'm exhausted and don't have as much time to devote to this as I normally do, so here are 3 problems that are tripping me up:. COVER, FELLOW, IEEE. We can calculate the covariance between two asset returns given the joint probability distribution. Print copies are available via CRC Press , Amazon , and elsewhere. (In particular, martingales play an. The point is that the order of events doesn't affect with respect to conditional probability. Ismor Fischer, 5/26/2016 4. For example, the scenario damages for a 3-foot flood are the expected damages and losses each time a 3-foot flood occurs at a particular site. To learn a formal definition of E[u(X)], the expected value of a function of a discrete random variable. Examples of expectation in a Sentence. This means that if you ran a probability experiment over and over, keeping track of the results, the expected value is the average of all the values obtained. The table below gives the names of the functions for each distribution and a link to the on-line documentation that is the authoritative reference for how the functions are used. a specific time interval, length, volume, area or number of similar items). Find the Expected Value of the spinner assuming you get the amount shown. We total the rows and columns as indicated. The expectation of a random variable is a number that attempts to capture the center of that random variable's distribution. Example 8 Here we use so that there is a still a long right tail but 90% of the weight is on the other side. In general, the same is true for the probability. • Expectation of the sum of a random number of ran-dom variables: If X = PN i=1 Xi, N is a random variable independent of Xi's. Toss a coin with probability p of heads. Let X= the number of samples that contain the pollutant in the next 18 samples analyzed. A concise explanation of the theory behind the calculator can be found here. Examples of convolution (continuous case) By Dan Ma on May 26, 2011 The method of convolution is a great technique for finding the probability density function (pdf) of the sum of two independent random variables. What is the expected profit? 3. The Law of Total Probability states that the payoff for a strategy is the sum of the payoffs for each outcome multiplied by the probability of each outcome. So we can now calculate the condition expectation, which, in this particular example, would be 1/3. If you are risk neutral, then you should be unwilling to sell this ticket for any amount of money less than its expected value, which is $10,000. " Probability anomalies in the tails should be regarded as rough estimates at best. You are dealt a poker hand. So the probability of having 4 or more accidents is 1 – 0. Multiply them and you get 64/132600 = 8/16575 =. Find the conditional probability? Solution: The total number of possible outcomes of rolling a dice once is 6. Hauskrecht Expected value Investment problem: • You have 100 dollars and can invest into a. The expectation maximization algorithm is a refinement on this basic idea. For example, a project team may identify risks and rate them according to the expert opinion of team members. Calculate the probability distribution and the expected value of the described game. Probability distributions are theoretical distributions based on assumptions about a source population. So there is no way an event or all the events totaled can have a probability of greater than 1. EL can be expressed as a simple formula:. If you roll a 2, 4, 5, or 6, you win $5. What is the expected number passing in two minutes? Find the probability that this expected number actually pass through in a given two-minute period. An opportunity to explore expected value through two way tables ( a potential examination combination). 232), (Sharpie, De Veaux,. Distributions 3. We begin with some preliminaries on measure-theoretic probability theory, which allows us to discuss the de nition. For example, if you have a coin, the probability of flipping the coin and it landing on heads or tails is 1. It is an appropriate tool in the analysis of proportions and rates. Evaluate the individual and cumulative probabilities of success in this case. Probability is a branch of mathematics, and a lot of people have trouble with math. Terminology and Examples Properties of Expectation Correlation The Method of Indicators Some Properties of the Normal Distribution Chebyshev’s Inequality and the Weak Law of Large Numbers CONDITIONAL PROBABILITY AND EXPECTATION Introduction Examples Conditional Density Functions Conditional Expectation Appendix: The General Concept of. Probability Example 1. 67 days (rounded). The expected value is what you should anticipate happening in the long run of many trials of a game of chance. Example Let be a random variable with support and probability mass function Its expected value is Expected value of a continuous random variable When is a continuous random variable with probability density function , the formula for computing its expected value involves an integral, which can be thought of as the limiting case of the summation. Probability Theory and Stochastic Processes Steven R. For example, if you have a coin, the probability of flipping the coin and it landing on heads or tails is 1. The expected value uses the notation E with square brackets around the name of the variable; for example:. High School: Statistics & Probability » Introduction Print this page. For example, take an electron on a hydrogen atom; the expectation value for all energy levels is at the nucleus even though many of the energy levels have 0 probability of being there. We will repeat the three themes of the previous chapter, but in a diﬀerent order. Suppose that (W,F,P) is a probability space where W = fa,b,c,d,e, fg, F= 2W and P is uniform. It is calculated by dividing one by the decimal odds. 53 for each bet of $10. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. Financial Economics Expected Utility Maximization Example of Substitution A: $5 with probability 1. Financial expectation probability questions - problem solving activities for teenagers. Strong Law. Pr(W) = 1 (2) 3. Discrete Random Variables. As we will see, the expected value of Y given X is the function of X that best approximates Y in the mean square sense. In the example in figure 2, the value for "new product, thorough development" is:. What is the probability to obtain 1 or 2 if I throw a dice once? 2. There are two outcomes (win and loss), each with its own probability. Expected Value. will study the conditional expected value of Y given X, a concept of fundamental importance in probability. If we plug into our formula expected value of X, is the probability 0. 1 Expected Value of Discrete Random Variables When a large collection of numbers is assembled, as in a census, we are usually interested not in the individual numbers, but rather in certain descriptive quantities such as the average or the median. 67 days is the expected time for this subproject. So notice the expected value is a value that the coin can't even take. Let's return to the Then, when the mathematical expectation E exists,. Expected Value of a Function of a Continuous Random Variable Remember the law of the unconscious statistician (LOTUS) for discrete random variables: $$\hspace{70pt} E[g(X)]=\sum_{x_k \in R_X} g(x_k)P_X(x_k) \hspace{70pt} (4. Expectations Expectations. If they pick mine, the sponsors give me $100. example, if X(t) is the outcome of a coin tossed at time t, then the state space is S = {0,1}. Another Example: Mixtures Suppose we have two hats: one has 4 red balls and 6 green balls, the other has 6 red and 4 green. Expectation. Example 36. This is the population mean. A further modification is necessary for development wells and projects. • What is the expected value of your investment? • M. The probability that Y takes on some value in a set A can be expressed as an expectation using the indicator function: P(Y 2A)=E(IfAg(Y)) (3) where IfAg(Y) is the indicator function that takes the value 1 when Y 2Aand 0 when Y 62A. Laws of Large Numbers 1. The probability of winning is 1 out of 350, because each ticket has an equal chance of being picked. ANS: 14/19. Probability and statistics symbols table Symbol Symbol Name Meaning / definition Example P (A) probability function probability of event A P (A) = 0. the degree of probability that something will occur: There is little expectation that he will come. The first prize for a raffle is $5,000 (with a probability of 0. Expected monetary value calculation relies on measuring the probability and impact of each risk. As you can see, these numbers do check out. How to use expectation in a sentence. For any continuous random variable with probability density function f(x), we. If it contains an Ace you get your $2 back, plus another $1. What is a fair price to pay for a single ticket in this raffle? Exercise 4. Expected Value of a Function of a Continuous Random Variable Remember the law of the unconscious statistician (LOTUS) for discrete random variables: $$\hspace{70pt} E[g(X)]=\sum_{x_k \in R_X} g(x_k)P_X(x_k) \hspace{70pt} (4. Pre-Algebra giving you a hard time? Shmoop's free Basic Statistics & Probability Guide has all the explanations, examples, and exercises you've been craving. Strong Law. An example would be rolling a 2 on a die and flipping a head on a coin. where p i is the probability of the occurrence of the value of x i. In a board game, players take turns spinning a wheel with 4 spaces and values of $100, $300, $400, $800. These examples may make EMV look simple but larger projects will have much larger data sets and be more difficult to compute. The expected value is a single average value that summarizes a probability distribution. When you finish, you'll have calculated expected values for each step of your entire project schedule. Expectation and Variance The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. , discounted at the riskless rate: call option: Class Problem: Price the put option with payoffs K u =2. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Ch5: Discrete Probability Distributions Santorico - Page 161 Expectation Another concept closely related to the mean of a probability distribution is the concept of expectation. For the example, 16 days / 6 is 2. f, then the right hand side of (1. 4, JULY 198 1 483 Maximum Entropy and Conditional Probability JAN M. The expected value can never be a value from the exact value of x. lists) of random variables, X and Y , and a function g ( X,Y ) of them both, the conditional expectation of g ( X,Y ) given X is a function. Probability, Expected Payoffs and Expected Utility • In thinking about mixed strategies, we will need to make use of probabilities. One set of rules that must always be followed in calculating expected return is that every outcome must have a probability assigned that might be 0. Beginning with a concrete example, let n= 8, and the outcome success, fail, fail, success, fail, fail, success, fail. Laws of Large Numbers 1. Equally Likely Outcomes "Outcomes that have an equal chance of occurring" (Collins, Cuevas, Foster, Gordon, Moore-Harris, Rath, Swart, & Winters, 1998). A subject repeatedly attempts a task with a known probability of success due to chance, then the number of actual successes is compared to the chance expectation. But conditional probabilities can be quite slippery and require careful interpretation. So, in this case, you'd divide 1 by 6 to get 0. Example: The time between failures of a laser machine is exponentially distributed with a mean of 25,000 hours. the expected number of successes in nBernoulli trials is np. Pre-Algebra giving you a hard time? Shmoop's free Basic Statistics & Probability Guide has all the explanations, examples, and exercises you've been craving. 0 Pr(X) 1 (1) 2. Find the probability that in the next 18 samples, exactly 2 contain the pollutant. It is the ratio of the number of ways an event can occur to the number of possible outcomes. : VaR (99%, 1 day holding period) = 10 units -> How do I calculate a 90% Expected Shortfall (Mean of realisations above the 90% quantile)? What I would need is a simple and Excel-suitable formula and a nice citation of a paper (not a paper eleborating on the statistical features of ES whereof I have already found enough ;-) ). If Xand Yare continuous, this distribution can be described with a joint probability density function. In addition, we can use our ability to count to determine the probability mass function for S n. Example 11. When asked to find the probability of A and B, we want to find out the probability of events A and B happening. So, in this case, you'd divide 1 by 6 to get 0. Stock Price Expectations and Stock Trading Michael D. Then, with eight toothpicks in the center the expected value of the random variable is:. TEST(DataB; DataE) DataB is the array of the observations. Mathematical expectation, also known as the expected value, is the summation or integration of a possible values from a random variable. For example, one way to partition S is to break into sets F and Fc, for any event F. Take a coin flip. Expected value (EV) is a concept employed in statistics to help decide how beneficial or harmful an action might be. Borel-Cantelli Lemmas 4. A manufacturer of computer disks has a historical defective rate of. "Apart from presenting a case for the development of probability theory by using the expectation operator rather than probability measure as the primitive notion, a second distinctive feature of this book is the very large range of modern applications that it covers. Khan Academy is a 501(c)(3) nonprofit organization. Data Management and Probability, Grades 4 to 6 is a practical guide that teachers will find useful in helping students to achieve the curriculum expectations outlined for Grades 4 to 6 in the Data Management and Probability strand of The Ontario Curriculum, Grades 1–8: Mathematics, 2005. 1 Examples Let’s go through several example. Random Variables 4. Second example computing an expected value. Posted on February 13, 2014 by Jonathan Mattingly The Probability Workbook is powered by WordPress at Duke WordPress Sites. For example, let X = the number of heads you. Craps Math. What is the probability that in a batch of 1000 disks, 2 would be defective? (note: answer using either the relevant probability table in the back of the book, or use the relevant probability function on your calculator / Excel). b) The probability the shirt will not be gold is 6 4 or 3 2. What is the probability that a car's transmission will fail during its ﬁrst. DataE is the range of the expected values. 0 Pr(X) 1 (1) 2. , a function mapping a probability space into the real line. Synonyms for expectation at Thesaurus. Expected Value The expected value of a game or procedure is the average value of. When a ﬂock of ducks ﬂies overhead, the hunters ﬁre at the same time, but each chooses his target at random, independently of the others. The concept of expectation can be easily understood by an example that involves tossing up a coin 10 times. In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability = −, that is, the probability distribution of any single experiment that asks a yes–no question; the question results in a boolean-valued. Where you are calculating the value of uncertain outcomes (circles on the diagram), do this by multiplying the value of the outcomes by their probability. Expected value highly depends on the probability, which is a subjective thing. In a sample space of equiprobable outcomes, the probability of an event is the ratio of the number of favorable outcomes to the total size of the space. What is the probability of the occurrence of a number that is odd or less than 5 when a fair die is rolled. probability self-study variance conditional $$ Expected value can be fairly easy via both method, we just. If you are risk neutral, then you should be unwilling to sell this ticket for any amount of money less than its expected value, which is $10,000. † In the SST example, the model gives us a probability distribution for the temperature at diﬁerent locations in the tropical. Students in Statistics and Probability take their understanding of probability further by studying expected values, interpreting them as long-term relative means of a random variable. Unexpected Loss (UL) – it is kno wn as the variation in. We total the rows and columns as indicated. We start with an example. Probability generating functions, use in calculating expectations. Properties of the Integral 6. In many cases, a risk probability is an educated guess that is modeled with a rating system such as low, medium and high probability. Moment) of all orders, in particular, the variance. For any continuous random variable with probability density function f(x), we. 05), then it is usually considered possible, in directing. Example 6-2: A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Given that the second heads occurs the expected value, and the. Note that E(XjY) is a random variable whereas E(XjY =y) is a number (y is ﬁxed). 11 If we toss a coin 1000 times and find that it comes up heads 532 times, we estimate the probability of a head coming up to be 532 1000 0. Xi's have common mean µ. Expected Value and Variance Have you ever wondered whether it would be \worth it" to buy a lottery ticket every week, or pondered questions such as \If I were o ered a choice between a million dollars, or a 1 in 100 chance of a billion dollars, which would I choose?" One method of deciding on the answers to these questions. So, firstly, the laws of probability, definition that probability is the relative likelihood that a particular event will occur. 1 Examples Let's go through several example. So you have learned the difference between a metaphor and simile or how to distinguish a transitive from an intransitive verb with the help of YourDictionary’s Grammar section. 10/40 An Introduction to Basic Statistics and Probability - p. For example, the expected value of rolling a six-sided die is 3. Example Articles & Resources. has expectation and variance given by the formulae E(X)= b+a 2 and V(X)= (b−a)2 12 Example The current (in mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0,25]. Often expectations. What is the probability distribution of the throw of a dice? 3. Pre-Algebra giving you a hard time? Shmoop's free Basic Statistics & Probability Guide has all the explanations, examples, and exercises you've been craving. Shapes of data distributions and probability distributions are described by the same terms-symmetric and skewed-so the context of such descriptions must be made clear. 8) will be on midterm exam 2, not midterm exam 1. Whether you are starting from scratch or if you are in a statistics class and struggling with your assigned textbook or lecture material, this workshop was built with you in mind. Probability 3. The mathematical expectation will be given by the mathematical formula as, E (X)= σ (x 1 p 1, x 2 p 2, …, x n p n ), where x is a random variable with the probability function, f (x),. The only remaining consequence in Example 3. It was, for example, used by the Dutch mathematician Christiaan Huygens in his short treatise on games of chance, published in 1657. For example, on the first flip, you have a 50% chance of winning $2. What is the probability of exactly two heads showing up? Is this a binomial experiment? n identical trials? Two outcomes, success/failure? Probability of success does not change? Trials independent? _____ Our interest is in the number of successes out of n trials. 5th Edition Version 5. We also de ned the theoretical variance of a random variable. 11/40 Example What is the expected. You want to calculate the probability (Poisson Probability) of a given number of occurrences of an event (e. It can be interpreted as the long-run average of many independent samples from the given distribution. (A few quick calculations based on. (Note that a is an outcome,. 1 In 1738, Daniel Bernoulli wrote: \Somehow a very poor fellow obtains a lottery ticket that will. Recall the coin toss. A discrete probability distribution consists of the values of the random variable X and their corresponding probabilities P(X). Probability refers to the possibility of occurrence of a condition or an event. Expected Value 7. The conditional expectation (also called the conditional mean or conditional expected value) is simply the mean, calculated after a set of prior conditions has happened. For example, instead of relying on a single net present value, companies calculate NPVs under a range of scenarios: say, base case, worst case and best case, estimate probability of occurrence of each scenario, and weighs the NPVs calculated according to their relative probabilities to find the expected NPV. 01 10,000 0. Risk-Neutral Probabilities 6 Examples of Risk-Neutral Pricing With the risk-neutral probabilities, the price of an asset is its expected payoff multiplied by the riskless zero price, i. They will also be used in the theory of convergence. 4, or $90 with probability 0. In probability, the average value of some random variable X is called the expected value or the expectation. As depicted by above diagram, sample space is given by S and there are two events A and B. 2 the class GPAs (2. It is the ratio of the number of ways an event can occur to the number of possible outcomes. customers entering the shop, defectives in a box of parts or in a fabric roll, cars arriving at a tollgate, calls arriving at the switchboard) over a continuum (e. If we plug into our formula expected value of X, is the probability 0. Example: the probability distribution for the random variable (now called) D, the number on the face of a die after a single toss: μ = E(D) = 21/6 = 3. Another advantage of using Markov chains for these problems is that the method scales up quite easily. The probability of any proposition X is somewhere between 0 and 1. Repeat Steps 1 through 4 for each subproject in your PERT Chart. Both these numbers must be less than unity, so ρ ^ 2 ≠ ρ ^. 25 because one would expect in many tosses of two coins that about one-quarter of the results would show heads on both. 0 Pr(X) 1 (1) 2. Another example of hard work was determining the set of probabilities associated with a sum, P(X +Y = t). For example, we might measure the number of miles traveled by a given car before its transmission ceases to function. Sample Statistics x and s2) population mean = the “expected value” of the random variable X = the “arithmetic average” of all the population values. To find the mean of X, multiply each value of X by its probability, then add all the products. Examples 1. Addition Law for Compound Events: A or B 6. Identifying when a probability is a conditional probability in a word problem. Two of these are particularly important for the development and applications of the mathematical theory of probability. One example is the density \begin{gather*} \rho(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}, \end{gather*} which is graphed below. A simple example of Expected Value (EV) put into practice - if you were to bet $10 on heads in a coin toss, and you were to receive $11 every time you got it right, the EV would be 0. We would like to define its average, or as it is called in probability, its expected value or mean. To start practicing, just click on any link. Problem: Contingency Tables with Sparsely Populated Cells The usual approach to contingency tables is to apply the X 2 statistic to each cell of the table, where the expected value for each cell is calculated by the method described on the previous page. How to use expectation in a sentence. For example, the heights of male students in a college, the leaf sizes on a tree, the scores of a test, etc. Posted on February 13, 2014 by Jonathan Mattingly The Probability Workbook is powered by WordPress at Duke WordPress Sites. So far we only have de ned it for events and it was a number. I'm writing a post with 14 gambling probability examples because I think that examples are one of the easiest ways to teach something. In this lecture we shall brie y overview the basic theoretical foundation of DTMC. (In particular, martingales play an. a) Construct the probability distribution for a family of two children. 5th Edition Version 5. The Law of Iterated Expectation is useful when the probability distribution of both a random variable X X X and a conditional random variable Y ∣ X Y|X Y ∣ X is known, and the probability distribution of Y Y Y is desired. In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average. What is the sum of the probabilities in a uniform probability distribution? a. • Example: Suppose that the expected number of acci-dents per week at an industrial plant is four. Using the coin toss example, the probability that the coin toss will come up tails is 50%. In Example 4. Thus, the complete expectation of life for a life of exact age 20 is 40 years. Probability refers to the possibility of occurrence of a condition or an event. Evaluate the individual and cumulative probabilities of success in this case. When you finish, you'll have calculated expected values for each step of your entire project schedule.