Question

The random variable X has moment generating function

ϕX(t)=exp((9t)^2)/2)+15t)

Provide answers to the following to two decimal places

(a) Evaluate the natural logarithm of the moment generating function of 2X at the point t=0.62.

(b) Hence (or otherwise) find the expectation of 2X.

c) Evaluate the natural logarithm of the moment generating function of 2X+7 at the point t=0.62.

Answer 1

a)

MGF of X:

So, MGF of 2X is given by:

So,

Required value =

b)

Now,

We know that,

So,

c)

The MGF of 2X+7 is given by:

So,

Required value =