expectation of random variable

fmfreshman · February 1st, 2013, 12:17 pm

Hi, I am considering a problem. Suppose X, Y are two positive random variables, and if we have E(X^2)<E(Y^2)can we prove that E(X^2)<E(YX)<E(Y^2)? My intuition tells me it might be true under some conditions, could you please help me with that? Thanks.

isometry · February 1st, 2013, 12:56 pm

If they are independent, E[xy] = E[x]E[y] then use arithmetic > geometric > harmonic mean on the squares...I think it should work

Traden4Alpha · February 1st, 2013, 1:03 pm

Just think about the formula for R^2 and the bounds on that number.

fmfreshman · February 1st, 2013, 1:24 pm

Thanks, what will happen if X and Y are highly positive correlated?

Traden4Alpha · February 1st, 2013, 1:30 pm

What do you think will happen when X and Y are highly positive correlated, maybe even perfectly correlated? What does the formula for R^2 tell you?