Try showing that the function is monotonic increasing and using that, show that if CDF_X(p) > CDF_Y(p) for all p in [0,1] then E[X] > E[Y].
does anyone have an idea how to prove the following inequality
where is normally distributed with a non-negative mean and are constants with
is also a constant.
Thanks in advance
Unfortuanately, I do not completely understand your hint. The function is increasing and convex in
The expectation is given by
Or do you mean that I should consider the cdf of the function of r.v. ?
But now it does not hold