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Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (...

Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes.

(a) Find the joint density function of X and Y.

(b) Compute E(X) and the conditional expectation E(X|Y= 1).

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