# Random Variables

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)

https://brainmass.com/statistics/probability/random-variable-functions-11950

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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).

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)