Hello everybody,

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

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- Apr 24th 2013, 06:16 AMJujuCompare the expectation of two functions of same r.v.
Hello everybody,

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 - Apr 24th 2013, 10:11 PMchiroRe: Compare the expectation of two functions of same r.v.
Hey Juju.

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]. - Apr 25th 2013, 12:26 AMJujuRe: Compare the expectation of two functions of same r.v.
Thanks!

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

- Apr 25th 2013, 01:16 AMchiroRe: Compare the expectation of two functions of same r.v.
Yes, consider the CDF of the log function of the random variable. That was my initial intent and idea for you,