Show that this is the distribution of the number of

Question

The geometric (p) distribution on {0, 1, 2,  .. }. The geometric (p) distribution is often defined as a distribution on {0, 1, 2, ..  .. } instead of { 1, 2, 3, . . .}. A random variable W has geometric (p) distribution on (0, 1, 2, . ..) if

P(W = k q^kp         (k = 0, 1, . . )

a) Show that this is the distribution of the number of failures before the first success in Bernoulli (p) trials.

b) Find P(W > k)     (k = 0, 1, . . .)      c) Find E(W).      d) Find Vαr(W).