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,

justifying your answer in each case:

(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....