I'm doin revision questions and I came along this question:

CAn anyone help ?

1. Suppose that the discrete random variable X has a geometric distribution with parameter p (0 < p < 1). In other words, suppose that

P(X = k) = (1 - p)^(k-1) p for k = 1, 2..

Let Y = X - 1.

(a) Find P(Y >/ l) for each l = 0,1,2,

(b) Show that for all nonnegative integers s and t

P(Y >/ s + t |Y >/ s) = P(Y >/ t)

(c) Suppose that you are working in a call centre and let Y be length of time in seconds

that it takes you to answer a customer query.

(i) Describe the event {Y >/ s} in words.

(ii) Describe the result stated in (b) in words.

(Note that the result stated in (b) is called the "memoryless property")