stat272 (1 Viewer)

[Dash]

need help with an assignment qquestion

fx(x) = 1/(1+x^2)pi <=== cauchy pdf

Does X have expectations E(|X|^alpha) for some values of alpha? Define the values of alpha for which this expectation exists...

Alright i have aattempted this question but its too bloody weeird?

i thougth that if alpha is odd then the integral will be odd and so should E(X^alpha) where alpha is odd would equal 0. However, obviously E(X) doesnt exist.

For the even values of alpha im not sure except that E(X^2) = infinity??

can sum1 help us out....even a bit of a hint would help!??

thx...

 

[NightWolf_in_DC]

lol any chance someone can throw some help my way?
i'm at question 1a

i've got E[X^n] = sum(from 1 to infinity) x^n * fX(x)

and i just don't know how to simplify it

 

[bigredboof]

for 1a using direct method, simplify the factorials and manipulate the terms. Ultimately you end up with np x the sum of a binomial with n-1 trials. therefor the expected value is np