Let X(t) = N(t)

i=1 Xi where Xi , i ≥ 1 are independent and identically distributed with mean E[X], and are independent of {N(t), t ≥ 0}, which is a Poisson process with rate λ. For s

(a) E[X(t)|X(s)];

(b) E[X(t)|N(s)];

(c) Var(X(t)|N(s));

(d) E[X(s)|N(t)].