4. (10%) Let X have the pdf f(x) = 3x2, 0 ＜ x ＜ 1, zero elsewhere. Consider a random rectangle whose sides are X and (I-X). Determine the expected value of the area of the rectangle.

3. (10%) Suppose we are playing draw poker. We are dealt (from a well shuffled deck) 5 cards which contain 4 spades and another card of a different suite. We decide to discard the card of a different suite and draw one card from the remaining cards to complete a flush in spades (all 5 cards spades). Determine the probability of completing the flush.

4. (10%) Let X have the pdf f(x) = 3x², 0 ＜ x ＜ 1, zero elsewhere. Consider a random rectangle whose sides are X and (I-X). Determine the expected value of the area of the rectangle.

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