lec28 - 36-225 Handout for Lecture # 28 October 29, 2010 1....

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Unformatted text preview: 36-225 Handout for Lecture # 28 October 29, 2010 1. In the game of roulette a wheel with 38 numbered spaces (18 red, 18 black, 2 green) is spun and ball drops into one of the slots. Suppose Player 1 bets $10 on "Red" and Player 2 bets $10 that the result will be between 1 and 12. Let X be the amount Player 1 wins and Y be the amount Player 2 wins. The joint pdf of (X, Y ) is given by the following table: y x -10 +20 -10 14/38 6/38 +10 12/38 6/38 2. Two cards are randomly drawn one after the other without replacement from a deck of cards. Define: X - number of aces obtained in the first draw Y - number of aces obtained in both draws. Find PXY (x, y) 3. Consider the following joint p.d.f: PXY (x, y) = e-2 x+y x! y! x = 0, 1, 2, 3 . . . y = 0, 1, 2, 3 . . . > 0 (a) Show that PXY (x, y) is a legitimate joint pdf. (b) Find P (X = 0, Y = 0). (c) Find P (X > 0, Y > 0). 4. Suppose that the joint density function of (X, Y ) is given by: 1 (xy + 1) fXY (x, y) = 80 0 < x < 4, 0 < y < 4 otherwise 0 (a) Show that fXY (x, y) is a legitimate density function. (b) Find P (X 1, Y 1) ...
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