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# Random Variables

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Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let

U = (X/m) / (Y/n)

a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom).
b) Find the density of V = U / (1+U)

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#### Solution Preview

Please see the attachment.

Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let

U = (X/m) / (Y/n)

a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom).
Solution. Since X and Y are independent ...

#### Solution Summary

Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let

U = (X/m) / (Y/n)

a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom).
b) Find the density of V = U / (1+U)

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