PLEASE I NEED HELP FOR THIS QUESTION. KINDLY, GIVE ME A MORE DETAILED AND A STEP BY STEP APPROCAH TO THE SOLUTIONS. THANK YOU VERY MUCH. QUESTION (a) In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined as follows. With X as the random amount that it will have to pay in claims, the premium charged by the insurance company is In(E(eaX)) P = A where a is some specified 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 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up? Hint: Here we assume all of 52 tickets uwere sold out. The problem asks the probability that no mnore than50passengers show up (c) Let X be a random variable following Gamma(a, A), where a > 0 and A 0, find E(X2) using the pdf of X. Let K also be an variable with rate X > 0. Find E(K2) using the pdf of X. expoential random

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.