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

Question
Asked Sep 8, 2019
77 views

Please give me a detailed step by step approach for me to understand

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
help_outline

Image Transcriptionclose

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

fullscreen
check_circle

Expert Answer

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

help_outline

Image Transcriptionclose

In(E(e*)) .. eq 1 P = A Where a = Expected value is given by OO E(x) xf (x)dx

fullscreen
Step 2

f(x) for exponential distribution is given by

help_outline

Image Transcriptionclose

f (x)= AeAx 11 OO E (oPA) е «дхЛе-1xdx ealxexdx heAx(a-1) dx eAx(a-1)dx = A 0 aeAra-)10 λ(α-1) (ecoAa-1)-eo) (0-1) λ(α-1) λ(α-1) -1 1 (а — 1) (1—«) l

fullscreen
Step 3

By sustitut...

help_outline

Image Transcriptionclose

substituting E(eax) in eq 1 1 In P = A

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Probability

Other

Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: When two dice are tossed, find the odds in favor of getting a sum of 7.

A: Odds in favor:Odds in favor of a particular event are the ratio of number of favorable outcomes of t...

question_answer

Q: Three fair coins are tossed. The two possible outcomes for a single coin are​ heads, h, and​ tails, ...

A: Part (a):The sample space is the collection of all outcomes, if a random experiment is performed.In ...

question_answer

Q: A pair of dice is rolled, and the larger of the two numbers showing is recorded.  Find the expecrted...

A: Given that a pair of dice is rolled and the larger of the two numbers is noted.Total number of possi...

question_answer

Q: We are currently on set operations and ven diagrams and I’m a little confused about the relationship...

A: To count the number of elements in A' union B using the given information

question_answer

Q: The following problems refer to strings in A to Z.  (a) how many diffrent four letter strings are th...

A: In this question, we have to form a four letter strings using the letters A to Z.Since in this quest...

question_answer

Q: Let X and Y be two random variables with joint probability mass function: p(x,y) = 1/48 xy(1+y) ??? ...

A: The provided joint probability mass function is:

question_answer

Q: According to police sources, a car with a certain protection will be recovered 90% of the time. If 2...

A: Introduction:Consider the event of recovering a stolen car with the protection as a “success”.For a ...

question_answer

Q: Three components are connected to form a system as shown in the accompanying diagram. Because the co...

A: Sample space = {SSS, SSF, SFS, SFFF,FSS, FSF, FFS, FFF} a) As per the questionThere should be exactl...

question_answer

Q: A company is in the business of finding addresses of long-lost friends. The company claims to have a...

A: The distribution:The company claims to have 80% success rate. There are names of six friends for who...