Question

4 points) Let Z1,Z2,...,Z1 be 11 independent N(O, 1) variables, and let Provide answers to the following to two decimal places Part a) Evaluate the moment generating function Mz2 (t) of Z2 at the point 0.23 Part b) Evaluate the moment generating function My(t) of Y at the point t = 0.31 . Part c) Find the mean of Y. Part d) Find the variance of Y.

Answer 1

a)

this is chi-square distribution with one degree of freedom

mgf = (1 - 2t)^ (-k/2)

here k = 1

= (1 - 2t)^ (-1/2)

= (1 - 2* 0.23)^ (-0.5)

= 1.360827

b)

df = k = 11

mgf = (1 - 2t)^ (-k/2)

for t = 0.31

mgf = (1 - 2 * 0.31) ^ (-11/2)

= 204.73411

c)

E(Y) = k = 11

d)

Var(Y) = 2*k = 2*11 = 22

Please rate