课程: Probability Foundations for Data Science

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Conditional expectation

Conditional expectation

课程: Probability Foundations for Data Science

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Conditional expectation

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- [Instructor] Let's wrap up expectation by discussing conditional expectation. You've had some practice when working with expectation of two random variables, but often these variables are independent from each other. This is different, though, when it comes to conditional expectation. Conditional expectation is when the expected value of a random variable depends on the outcome of another random variable. For example, for random variable X and conditional random variable Y, the conditional expectation is denoted by E, then parenthesis, and then X, a bar, Y, and then another parenthesis. This is denoted as the expectation of X given Y. The concept of conditional expectation is the same for discrete and continuous random variables, but their corresponding equations are different. Let's begin with conditional expectation for discrete random variables. For discrete random variable X and Y, the conditional expectation of X given when Y is equal to a value Y, it is equal to the following…

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