Question: 13. For an integer n 3, let X be a random variable with the probability density function Such random variables have significant applications in

13. For an integer n ≥ 3, let X be a random variable with the probability density function

f(x) = r(n+1) / (1+2) -(n+1)/2

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).

f(x) = r(n+1) / (1+2) -(n+1)/2

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