Random Variable and its distribution.

(a) If the probability of a random variable X is given by

f (x) = k(x2 1), x = {1, 2, 3, , 20} then, what is the value of the constant k?

(b) Let X1, X2, X3 be three independent Bernoulli random variables with the same probability of success p. Let a new random variable Y = X1 + X2 + X3 has a sample space S

S = {FFF,FFS,FSF,SFF,FSS,SFS,SSF,SSS} whereS=success ,andF =failure. WhatisP(0Y 2)?