# PLEASE I NEED HELP FOR THIS QUESTION. KINDLY, GIVEME A MORE DETAILED AND A STEP BY STEP APPROCAH TOTHE SOLUTIONS. THANK YOU VERY MUCH.QUESTION(a) In deciding upon the appropriate premium to charge, insurance companiessometimes use the exponential principle, defined as follows. With X as therandom amount that it will have to pay in claims, the premium charged bythe insurance company isIn(E(eaX))P =Awhere a is somespecified positive constant. Find P when X is an expo-nential random variable with parameter A, and a = aX, where 0 a < 1(b) An airline knows that 5 percent of the people making reservations on a cer-tain flight will not show up. Consequently, their policy is to sell 52 ticketsfor a flight that can hold only 50 passengers. What is the probability thatthere will be a seat available for every passenger who shows up? Hint: Herewe assume all of 52 tickets uwere sold out. The problem asks the probabilitythat no mnorethan50passengers show up(c) Let X be a random variable following Gamma(a, A), where a > 0 andA 0, find E(X2) using the pdf of X. Let K also be anvariable with rate X > 0. Find E(K2) using the pdf of X.expoential random

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Step 1

Hello there! there are more than 1 question. According to our policies we cannot answer more than one question. So please find the solution for question a. If you have doubts in remaining question, kindly make a new request, mentioning the question in which you need help.

a) Given Distribution is a exponential distribution

We need to find the value of P

Step 2

f(x) for exponential distribution is given by

Step 3

By sustitut...

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