Question

Let a > 2. Suppose a discrete random variable X has the following probability
distribution:
p ( 0 ) = P ( X = 0 ) = c,
p (k) = P ( X = k ) = 1/(a^k), k = 1, 2, 3, … .
a) Find the value of c ( c will depend on a ) that makes this is a valid probability
distribution.
b) Find the moment-generating function of X, M( t ). For which values of t does it exist?
c) Find E ( X ).