A quick introduction to expected value formulas. Expected Value Formula. Stephanie Glen. Loading. The Expected Value of a bet shows us how much we can expect to win (on average) per bet, and as such is the most valuable calculation a bettor can make. How to Calculate an Expected Value. Expected value (EV) is a concept employed in statistics to help decide how beneficial or harmful an action might be. If one considers the joint probability density function of X and Y , say j x , y , then the expectation of XY is. A discrete random variable is a random variable that can only take on a certain number of values. You can think of an expected value as a mean , or average , for a probability distribution. This division is the only equitable one when all strange circumstances are eliminated; because an equal degree of probability gives an equal right for the sum hoped for. It uses estimated probabilities with multivariate models , to examine possible outcomes for a proposed investment. If the outcomes x i are not equally probable, then the simple average must be replaced with the weighted average, which takes into account the fact that some outcomes are more likely than the others. Check out the grade-increasing book that's recommended reading at top universities! It follows directly from the discrete case definition that if X is a constant random variable , i. For example, suppose we toss a coin where the probability of heads is p. Thanks probability share cite improve this question. Here's how it works: This makes sense with our intuition as one-half of 3 is 1. Figure out the possible values for X. Hypothesis Testing Lesson 9: More practically, the expected value of a discrete random variable is the probability-weighted average of all possible values. But finally I have found that my answers in many cases do not differ from theirs. Two variables with the same probability distribution will have the same expected value, if it is defined. Thus the expected value of X is.