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1. Consider the following distribution of (X Y) where X and Y ae both binary random variables: 1/4 i (a)-(0.0 1/4 if (x, y) (0,0) 1/8 if (r,y) (1,0) Jx3/8 if (r,)- (0,1) ,Y (z, y) = 1/4 if (, ) (11 (a) What is the probability density function of Y? (b) What is the expectation of Y1 (c) What is the variance of Y? (d) What is the standard deviation of Y? (e) Do the same to X. (f) What is the covariance between Y and X? (g) What is the correlation coefficient between Y and X? (h) Are X and Y independent? (i) What is the conditional probability density function of Y given X-0? G) What is the conditional expectation of Y given X-1?
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