Let X and Y be discrete random variables with joint

Chapter , Problem 20

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QUESTION:

Let \(X\) and \(Y\) be discrete random variables with joint probability mass function

\(p(x, y)=\frac{1}{e^{2} y !(x-y) !}, \quad x=0,1,2, \ldots, \quad y=0,1,2, \ldots, x\)

\(p(x, y)=0\), elsewhere. Find \(E(Y \mid X=x)\)

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QUESTION:

Let \(X\) and \(Y\) be discrete random variables with joint probability mass function

\(p(x, y)=\frac{1}{e^{2} y !(x-y) !}, \quad x=0,1,2, \ldots, \quad y=0,1,2, \ldots, x\)

\(p(x, y)=0\), elsewhere. Find \(E(Y \mid X=x)\)

ANSWER:

Step 1 of 3

Clearly,

where the last equality follows since  is the number of subsets of a set with  elements and hence is equal to .

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