Thread: Discrete

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")

is >/ supposed to be ?

I haven't done this one in years...



let w=k-(a+1), so the sum starts at zero






SO





At least my memory for this memoryless property is decent.