argent answered required

c) Let X and Y be two discrete random variables. We define Z = X + Y, i.e. Vwe Q, Z(w) = X(W) + Y(w). i) Show that: P(Z = z) = > fx.x(x,z-x) X ii) Now assume that X and Y are independent. Show that: P(Z = z) = > fx (x)fy(z -x) = > fx(z-y)fx(y) X From now on, we assume that X and Y are independent random variables which have the Poisson distributions with parameters Ax and dy , respectively. iii) Show that Z has the Poisson distribution, with parameter dx + ly . iv) Show that the conditional distribution of X , given X+ Y = n, is binomial, and find its parameters