Question

For both questions, demonstrating the result through Tchebytchev's Theorem(if its possible), please.

6)Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below:

T = -1 if X < -2

T = 0 if - 2 ≤ X ≤ 0

T = 1 if x>0

Find the moment generating function of T and, from it, calculate E (T) and Var (T).

9) An insurance company insures two types of vehicles, popular vehicles and vehicles
luxurious. The damages claimed as a result of an accident involving a popular car have
distribution N (7, 1) and the damages claimed as a result of an accident involving
luxury has an N (20, 6) distribution. Suppose the company receives three accident claims
of popular cars and a luxury car accident claim. Assuming that
these four complaints are mutually independent, what is the likelihood that the
total amount claimed for the three accidents involving popular cars exceeds the total
claimed by the accident involving the luxury car?

Answer 1