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(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

  1. (i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf

                    f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1   0 < x2 < 1

  1. , otherwise

            (ii) Calculate E(X1) and E(X2)    

(iii) Are the variables X1 ­and X2 stochastically independent?

  1. Given the variables in question 1, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].
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