# Thread: Convergence in probability and distribution

1. ## Convergence in probability and distribution

Let X be the random variable which takes the values 0 and 1 only and is such

that P[X
= 0] = P[X = 1] = 1/2. Define the sequence of random variables X, = X for all n and let Y = 1 - X. Now, answer the following,
(i) Does Xn, converges to X in probability?
(ii) Does Xn, converges to X in distribution?
(iii) Does Xn, converges to Y in probability?
(iv) Does Xn, converges to Y in distribution?

Ok so i know what the definitions are for both probabiltiy and distribution...i just don't know how to apply them to these types of questions??
Any kind of help would be helpful....

2. Are you creating a sequence of IID rvs $X_n$ or is $X_n=X$ ?

Also Y has the same distribution as X, BUT when X=0, Y=1 and visa versa.

3. It's equal to X.... Any ideas of how you would go about answering this type of question would be incredibly helpful!!