课程: Probability Foundations for Data Science

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Expectation of discrete random variables

Expectation of discrete random variables

课程: Probability Foundations for Data Science

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Expectation of discrete random variables

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- [Instructor] Let's start by learning about expectation for discrete random variables. Remember, a discrete random variable contains a finite or accountable number of values. For discrete random variables, the expectation is the weighted average of all possible outcomes for the random variable by summing up those values. Let's look at the formal equation used for finding the expectation of a discrete random variable. You'll have a discrete random variable with a finite list of possible values denoted by x1 to xk. Each of those possible values have a corresponding probability denoted by p1 to pk. The expectation is represented by the following equation where you sum each pair of values and their associated probabilities multiplied together. The probabilities of the random variable must all add up to equal exactly 1. This is represented by a p1 added to all the probability values until you get to pk, and again, that must equal 1. This then leads to the conclusion that the expectation…

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