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I am trying to find the distribution of the maximum of a set of independed Chi-square RV's with 2-degrees of freedom. Actually I only want to find the MEAN value.

I am using the following formula to find the PDF.

[tex]f_{X_{\mathsf{max}}}(x) = NF_X(x)^{N-1}f_X(x)[/tex]

Following PDF and CDF is used:

[tex]f_X(x)=\frac{1}{2}e^{-\frac{x}{2}}[/tex]

[tex]F_X(x) = 1-e^{-\frac{x}{2}}[/tex]

So what I want to find is: (Assuming N variables)

[tex]E[f_{X_{MAX}}(x)] =N \int_0^R xF_X(x)^{N-1}f_X(x)[/tex]

I am stuck in a neverending integration by-parts.

If anybody know any solution to this or any method to find this, please let me know.

Cheer.s

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# Maximum of Chi-square RV's

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