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

f(x)=&(x-a)exp((-(x-a)^2)/b) where a and b are constants

2. Relevant equations

find & in terms of b:

show that the expected value of X is given by

X=a + sqrt(pi*b/4)

identity given

x(x-a)=(x-a)^2+a(x-a)

and integral from 0 to infinity of x^2*exp-x^2 dx=sqrt (pi) /4

3. The attempt at a solution

i found &=2/b and thought my solution was coherent but seeing as i cant answer the next question im confused as to where i went wrong .

i manage to find X= a + sqrt(pi/4) but cant get that b into the square root no matter what i try .

i separated into 2 integrals using the first identity then set Y=(x-a)/sqrt b and used the second identity to get sqrt (pi /4)( the other integral giving the expected a)

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

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

# Homework Help: Probability density functions

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