Problem B . Suppose that ( X 1 , X 2 ,. ) are independent identically distributed ran dom variables with probability mass function f ( 20 ) = ( 1 - P...

Suppose that {X1, X2, . . .} are independent identically distributed random variables with probability mass function f(x) = (1 − p)x p

Problem B . 4 . Suppose that ( X 1 , X 2 ,. ) are independent identically distributed random variables with probability mass functionf ( 20 ) = ( 1 - P ) p for a = 0 1 2( a ) Derive the mean and variance of X( b ) Let S = 1 , Xi and find a sequence of constants ( an On ) such that InIn an converges in distribution to a non- degenerate random variable WV as non0 . You need to prove the convergence and identify WV .