Answer to Question #239140 in Statistics and Probability for rawr

Question

1. If 𝑋~𝑡(𝑘) , then 𝐸[𝑋] = 0 if 𝑘 > 1 and 𝑉𝑎𝑟[𝑋] = 𝑘 𝑘−2 if k >2
2. If X is an F – distributed random variable with m and n degrees of freedom, then 𝑉𝑎𝑟[𝑋] = (2𝑛^2(𝑚+𝑛−2))/(𝑚(𝑛−2)^2(𝑛−4)).
3. If X has a chi-square distribution, then 𝑚𝑋(𝑡) = [ (1/2)/((1/ 2)−𝑡 )] ^(𝑘/2) = [ (1)/(1−2𝑡) ] ^(𝑘/2) , t < ½.