Question: Conditional Expectation given a indicator random variable Let Y be a discrete random variable, A be an event with 0 < P(A) < 1, and

Conditional Expectation given a indicator random variable

Let Y be a discrete random variable, A be an event with 0 < P(A) < 1, and IA be the indicator random variable for A.

(a) Explain precisely how the random variable E(Y | IA ) relates to the numbers E(Y |A) and E(Y |AC).

(b) Show that E(Y |A) = E(Y IA)/P(A), directly from the definitions of expectation and conditional expectation.

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