Let X have a geometric distribution with parameter p, 0 (1) Determine the z-transform of X and by means of it E(X) and Var(X). (2) Let X1 and X2 be independent random variables, identically...

Let X have a geometric distribution with parameter p, 0 <><>

(1) Determine the z-transform of X and by means of it E(X) and Var(X).

(2) Let X1 and X2 be independent random variables, identically distributed as X. Determine the z-transform of Z = X₁
+ X₂
and by means of it E(Z) and Var(Z).

Verify the 2nd moment obtained in this way by another method.