If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter 1 and

Question:

If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter θ1 and the other n2 random variables have Bernoulli distributions with the parameter θ2, show that, in the notation of Exercise 8.4,
(a) E(Θ1 – Θ2) = θ1 – θ2;
(b) var(Θ1 – Θ2) = θ1(1– θ1)/n1 + θ2(1– θ2)/n2 .