Question

The profit (in millions) of Great Life Insurance Company for 2017, X, follows a distribution with
moment generating function
MX (t) = exp (100t + 200t^2) . Due to business expansion, its profit for 2018 is Y = 1.15X − 6.
(a) Determine the expected profit of Great Life Insurance Company for 2018.
(b) Calculate the probability that the profit for 2018 is at most 130, given that the profit in the year is at least 100.

Answer 1

As moment generating function uniquely describes the distribution of a random variable

and moment generating function of normal distribution is

Comparing with given moment generating function we get we conclude that X has normal distribution with

a) Hence using property of expectation we have

b) Also variance of Y is

Define the standard random variable Z as

Then using normal table we have the required probability as