Try find relationship between E(Π(Π-E(Π))) and var(Π)

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You need to show us your work, and show us where you're stuck, before we can help you. Also, please post homework questions in the appropriate Homework Help forum.

- Warren
 
chroot said:
You need to show us your work, and show us where you're stuck, before we can help you. Also, please post homework questions in the appropriate Homework Help forum.

- Warren

thanks for the reply, there is no homework questions associate with this, all I need is trying to prove there is relationship between E(Π(Π-E(Π))) and var(Π), and not nesserary equal but other relationship like exponential relationship. anybody can help
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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