Let X 2 2 a Using the moment generating function show that t

Let X ^2 *(2). (a) Using the moment generating function, show that the mean and variance are 2 and 4. (b) Compute P(X > 2).

Solution

(a)

n=2

The chi-square distribution has the following properties:

Therefore,

Mean = 2 Answer

Variance = 2*2 = 4 Answer

(b)

Critical Value =3.841

alpha =0.05

dF=1

P-value = 1 - 0.95

= 0.05 Answer