(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A density function used is:

[tex]f(y) = \frac{2y}{\theta}e^{\frac{-y^{2}}{\theta}} y > 0[/tex]

using method of transformations find:

(a) pdf of U = Y^2

(b) E(Y) and V(Y)

2. Relevant equations

f(u) = f(h^-1(u))*|dh^-1/du|

h^-1(u) = sqrt(u)

3. The attempt at a solution

The pdf Y^2 ~ exp(theta)

E(Y) = E(U^1/2).

That is:

[tex]\int\frac{1}{\theta}u^{1/2}e^{\frac{-u}{\theta}}[/tex]

So, multiply by sqrt(theta)/sqrt(theta) and group terms...

[tex]\frac{\sqrt{\theta}}{\theta}\int\sqrt{\frac{u}{\theta}}e^{\frac{-u}{\theta}}[/tex]

The integral is the Gamma function with parameter 3/2. So I get...

sqrt(PI/THETA)/2 as the answer....but a little internets research reveals the expected value *should* be sqrt(PI * THETA)/2. I can't find out where my math went wrong, it's something stupid but I've been stuck for a whole day...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Expected value of Rayleigh

**Physics Forums | Science Articles, Homework Help, Discussion**