Let X Uniform(0; 1). Given that X = x, let Z;Z1;Z2 be i.i.d. dened by P(Z =

1jX = x) = x; P(Z = 0jX = x) = 1 ? x.

Let X ~ Uniform(0, 1). Given that X = x, let Z, Z1, Z2 be i.i.d. defined by P(Z = 1 X -x) = x, P(Z = 0|X = x) =1 -x. a) Find P(Z1 + Z2 = 1). b) Find E(Z1). c) Find E(ZIZ2). d) Are Z1 and Z2 independent RVs