Question: Please help me to do Q3 and Q4 with steps. Q3 (12 marks) Let X has a uniform distribution on the interval (0,1). Give that

Please help me to do Q3 and Q4 with steps.

Q3 (12 marks) Let X has a uniform distribution on the interval (0,1). Give that X=x, Yhas a uniform distribution on the interval (0,x). Find the marginal p.d.f. of Y. Q4. (12 marks) Suppose that X follows Gamma distribution with parameters a=2,0=2. And Y follows Gamma distribution with parameters a=4,0=2. Assume that X and Y are independent. Find the probability P(Z>21) where Z=X+ Y

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