Please answer the following question.

QUESTION 6 [10] 6.1 The moment generating function (mgf) of the chi-square distribution with parameter n is given by M (t) = (1 - 2t ) in. Use differentiation to find the mean and the variance. (4) 6.2 Suppose that the probability density function (pdf) of X is given by fx (x) = le Lx x20 0, otherwise with 1 > 0. For the variable X, determine the 6.2.1 cumulative distribution function. (3) 6.2.2 moment generating function (mgf). (3)