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Let X be a uniform random variable on [0,1] and conditional on X=x. Let Y be an exponential random variable with mean x. a) find
Let X be a uniform random variable on [0,1] and conditional on X=x. Let Y be an exponential random variable with mean x.
a) find the joint density of X and Y
b) find E[Y]. (for this one the answer is 1/2, but I want know how to get it, please be detail )
c) find Var[Y].(answer is 5/12)
d)find cov(X,Y).(answer is 1/12)
Please show every step
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