1. ## Convergence in probability

Hi I have a question:

So suppose that
P(Yn = k) = (1 - 2-n-1)-1 / 2k+1 for k=0,1,...n.
And Y~ geo(1/2)
How do I show that Yn converges in distribution to Y?

I know I have to incorporate the PMF of the geometric distribution which is px(k) = P(X=k) = (1-p)k-1p

2. ## Re: Convergence in probability

Convergence in probability and convergence in distribution are two different thing. If you are in fact meant to show CID, all you need to do is - for an arbitrary k - show that P(Y_n = k) = 1/2^(k+1) as n goes to infinity, which really shouldn't be that hard.

To show CIP , you need to state what the r.v. Y_n is meant to converge to (for example the sample mean converging to the population mean).