In probability theory, the expected value of a random variable, intuitively, is the long-run The expected value is also known as the expectation, mathematical Definition · General definition · Properties · Uses and applications. 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. Loading web-font TeX/ Math /Italic Expected Value (i.e., Mean) of a Discrete Random Variable We then add these products to reach our expected value. A quantity equal to the average result of an experiment after a large number of trials. The compuational formula will give you the same result as the conceptual formula above, but the calculations are simplier. Sampling Distributions Lesson 7: The expected value is a key aspect of how one characterizes a probability distribution ; it is one type of location parameter. In this case, the values are headed towards 2, so that is your EV. So you have a one half chance of having to pay 25 dollars. The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points , which seeks to divide the stakes in a fair way between two players who have to end their game before it's properly finished. A notable inequality concerning this topic is Jensen's inequality , involving expected values of convex or concave functions. Dies folgt aus dem Satz über die beste Approximation, da. One example sequence of ten rolls of the die is 2, 3, 1, 2, 5, 6, 2, 2, 2, 6, which has the average of 3. Definition, Word Problems T-Distribution Non Normal Distribution Chi Square Design of Experiments Multivariate Analysis Sampling in Statistics: Set this number aside for a moment.