Homework 9 - fth ip, what is the frequency function of...

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550.420 Introduction to Probability Fall 2011 Homework 9 Due Thursday November 3, 2011 1. (2 points) Suppose X and Y have joint density f X,Y ( x, y ) = 1 2 e - y I (0 , ) ( y ) I ( - y,y ) ( x ) . Compute P [ X 1 | Y = 3]. 2. (2 points) Suppose X and Y have joint density f ( x, y ) = 1 2 (3 x 2 + 4 xy ) I (0 , 1) ( x ) I (0 , 1) ( y ) . Find the marginal density of X and the conditional density of Y given X = x . 3. (2 points) First a point Y is selected at random from the interval (0,1), then another point is selected at random from the interval ( Y ,1). Find the probability density of X . 4. (2 points) A fair coin is ±ipped until the sixth head is obtained. If the third head occurs on the
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Unformatted text preview: fth ip, what is the frequency function of number of ips? 5. (2 points) Let-1 / 9 < c < 1 / 9 be a constant. Let p X,Y ( x, y ) be given by the following table: Y X-1 1-1 1 9 1 9-c 1 9 + c 1 9 + c 1 9 1 9-c 1 1 9-c 1 9 + c 1 9 (a) Show that the frequency function of X + Y is the convolution of the frequency functions of X and Y for all c . (b) Show that X and Y are independent if and only if c = 0. 1...
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