Recent content by batman3

There is no context and/or further background. It was just a question that came to my mind while studying convergence of random variables. I just thought a normalized sequence would always have mean 1 in the limit and I was wondering whether there would be a general condition when it converges.

So what should be the restriction on the X_i's? In particular, can the Y_i's still convergence if the X_i's go to infinity?

Let X_1, X_2, ... be a sequence of random variables and define Y_i = X_i/E[X_i]. Does the sequence Y_1, Y_2, ... always convergence to a random variable with mean 1?