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Joint Probabilities

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let

T = Z / √ (V/n)

Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)

Solution Summary

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let

T = Z / √ (V/n)

Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)

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