STAT W21 Lecture Notes - Lecture 21: Random Variable, Hypergeometric Distribution, Weighted Arithmetic Mean
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In repeated independent trials with probability "p" of success in each trial, the chance that the. As "n" increases, for every number e > 0, p(|(fraction of successes in "n" trials) - p | < e) fraction of successes is close to "p" grows as the number of trials grows approaches 100% In games of chance you should expect the fraction of times you win to approach the chance of winning each game. The long-run limiting average of the values "x" takes in repeated trials. Analogous to the mean of the list: it is the balance point of the probability histogram. The expected value of a discrete random variable "x" can be calculated from the probability distribution of "x" (average of the labels on the tickets in the box) means the average of the list of numbers on all the labels, including repeated values as many times as they occur.
