Question: 12. For an integer n 3, let X be a random variable with the probability density function f (x) = 0 *n + 1

12. For an integer n ≥ 3, let X be a random variable with the probability density function f (x) = 0 *n + 1 2 , √nπ 0*n 2 , * 1 + x2 n ,−(n+1)/2 , −∞ < x < ∞. Such random variables have significant applications in statistics. They are called t-distributed with n degrees of freedom. Using the previous two exercises, find E(X) and Var(X).

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