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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 37E
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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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