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Chi-Square Distribution

Posted 10 years ago

Let Xi; i = 1; 2 be independent random variables (i.r.v.'s) having a Chi-square distribution, EXi = 4.

Using characteristic functions and the inversion formula and the probability density function (pdf) of Y = X1 -X2:

Find E(Y^8)

How do i run all these computations on mathematica?? Can someone give me a lowdown on where to begin and finish?

POSTED BY: Jim Kim
2 Replies
Posted 10 years ago

This is the short way (so compare your eventual answer with this result):

Expectation[(x - y)^8, {x \[Distributed] ChiSquareDistribution@4, y \[Distributed] ChiSquareDistribution@4}]

The [Distributed] character is entered esc dist esc

POSTED BY: Bruce Colletti
Posted 10 years ago

Thank you Bruce, I'll give it a shot now.

Do you have any approach to finding the probability density function of Y = X1 - X2 by char functions and inversion form?

POSTED BY: Jim Kim
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