Y is a random variable that has a Student t distribution with n degrees of freedom. VarO') = EO'Z) E2 (Y) So, Z Z is a standard normal random variable and U is a chi square random variable with 11 degrees of freedom U and Z are independent. lTherefore, Y: 22 2 " \"a TI. Z 2 is a square of a random variable with standard normal distribution, which is the chi square random variable with one degree of freedom. Applying that E G) = E (X)E G) is true for all independent random variables X and Y provided Y at 0, 1 50\") = 1'15 (Z 2)1? (5) Given that the mean = 11. 13(22): 2? Replace the 2? above with the correct number