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3. Suppose Y is normally distributed with mean X and variance o2 = 4 and X is uniformly distributed on [0, 6]. Find (a) the

3. Suppose Y is normally distributed with mean X and variance o2 = 4 and X is uniformly distributed on [0, 6]. Find (a) the unconditional density function for Y, (b) E[Y], (c) V(Y). Ans. (a) fy(y) = 12 /2T Jo e - ( y - 2 ) 2/ 8 dx ( b ) 3 ( c ) 7

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