Hi guys,

I hope you might be able to help me with this question:

Suppose X_n are independent, and X_n \rightarrow X in probability. Show that X is almost surely a constant.

The hint I got was: Suppose that X is not a constant almost surely. Can there be a and b with a<b, such that P(X<a)>0 and P(X>b)>0 ? Now use independence of X_n and X_n+1.

I really have no idea where to go with this so any help would be much appreciated! PS. Sorry about the bits not written out in Latex - it kept saying Latex compile error whenever I submitted them.

Many thanks,