Question: LetY1andY2are random variables. Given that the value ofY2=y2, the conditional distribution of (Y1|Y2=y2)Unif(0, y2) . We also know thatY2Gamma(1,1) (the marginal distribution ofY2).(This is only

LetY1andY2are random variables. Given that the value ofY2=y2, the conditional distribution of (Y1|Y2=y2)Unif(0, y2) .

We also know thatY2Gamma(1,1) (the marginal distribution ofY2).(This is only for part a, b)

  1. FindE(Y1).
  2. FindV(Y1).
  3. X1Gamma(1,2), findE(X13).
  4. X2Normal(1, 2^2). Let (x) be the cdf function of standard normal distribution, use () function to express the probability thatX2is between1 to 3.

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