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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

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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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
Transcribed Image Text: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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