Question: (*) Prove that for the collective risk model (S) = (X) (N) and that ????(S) = (N) ????(X) + ????(N) (X)2 using the moment generating

(*) Prove that for the collective risk model (S) = (X) (N) and that ????(S) = (N)

????(X) + ????(N) (X)2 using the moment generating function MS(t) of S. In the formulae above, N, X and S are the random variables for the number of claims, the severity, and the aggregate losses, respectively.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Insurance Questions!

Please Help! I've got this due on saturday. Please read the instructions carefully. A new client of yours, Katie Perez wants to open an ice cream shop near the downtown shopping center. She will...

I NEED HELP ASAP.BE SURE TO ANSWER 3.64. (a) Find the moment generating function of a random variable X having density function (b) Use the generating function of (a) to find the first four moments...

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

The purpose of this exercise is to prove the following Vapnik-Chernovenkis bound: for any finite class $\mathscr{G}$ (containing only a finite number $|\mathscr{G}|$ of possible functions) and a...

4.35. Let X1 and X2 be independent random variables that are chi-square distributed with v1 and v2 degrees of freedom, respectively, (a) Show that the moment generating function of Z X1 X2 is ,...

please assist me to solve the questions below. Give precise explanations The distributions of aggregate claims from two risks, denoted by S, andS,, are as follows: S, has a compound Poisson...

Kindly solve the following questions by giving precise explanations The distributions of aggregate claims from two risks, denoted by S, andS,, are as follows: S, has a compound Poisson distribution...

Please explain to me clearly and show how to do the two suppositions in the (question) file. Please take a look at the (notes) file and see the material up to the questions will be needed to answer...

Tukey's HSD test Sleep apnea is a disorder characterized by pauses in breathing during sleep. Children who suffer from untreated sleep apnea often have behavior problems, including hyperactivity,...

Given: . Probability Density Function (PDF): 0(1 -2)0-1 if0 0 is an unknown parameter. Based on these observations, determine an estimate of & using (a) maximum likelihood (b) method of moments 2....

May I seek you help for the following questions about loss models application and probability, please? Thank you. Problem 1 (Required, 25 marks) (a) We let X be a non-negative continuous random...

What advice would you give an entrepreneur who was trying to finance a start-up? Why would most employees of small firms welcome a leadership approach that sought their ideas and involved them in...

Financial frauds perpetrated by companies such as Enron, WorldCom, and Adelphia led to the passage of the Sarbanes-Oxley Act of 2002. Using the Internet, find answers to the following questions about...

7-3 A methods analysis has been made of a certain activity at a cost of $750. It is proposed that changes be made in the existing method which will yield an annual saving in material costs of $2,400....

The Barboa Fund can be best described as a fund segmented by: A. size/style. B. geography. C. economic activity. Three years ago, the Albright Investment Management Company (Albright) added four new...

Discuss the use of testimonials in advertising. Which of the four AIDA steps might testimo nials accomplish? Are they suitable for all types of products? If not, for which types are they most...

Discuss the future of smaller advertising agencies now that many of the largest are merging to form mega-agencies.

Does advertising cost too much? How can this be measured?

Exercise 8-6A (Algo) Effect of issuing common stock on the balance sheet LO 8-2, 8-4 Newly formed S&J Iron Corporation has 93,000 shares of $5 par common stock authorized. On March 1, Year 1, S&J...

J had the following transactions: 6/1/20 Sold ABC stock for $2,700 with a $200 sales expense. The stock was purchased 2/1/20 for $3,000. 6/1/20 Sold FGH stock for $8,150 with a $150 sales expense....

Mountain Cycles started October with 15 bicycles that cost $75 each. On October 10, Mountain purchased 25 bicycles at 501 each. On October 31, Mountain sold 23 bicycles for 507 each Requirements 1...