Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

An insurance company issues a policy covering losses up to 5 (in thousands of dollars). The loss, $X$ , follows a distribution with density function:$$f(x)=\left\{\begin{array}{cc}{\frac{3}{x^{4}}} & {x \geq 1} \\ {0} & {x<1}\end{array}\right.$$What is the expected value of the amount paid under the policy?

02:54

Fan Y.

Intro Stats / AP Statistics

Chapter 3

Continuous Random Variables and Probability Distributions

Section 9

Supplementary Exercises

Continuous Random Variables

Piedmont College

Cairn University

Oregon State University

University of St. Thomas

Lectures

03:48

Insurance Reimbursement An…

04:25

04:12

Insurance An insurance pol…

04:49

13:09

05:36

Losses After Deductible A …

05:10

Insured Loss An insurance …

06:30

01:58

Determine which are probab…

20:26

01:36

Suppose a homeowner spends…

04:51

The probability distributi…

04:11

Let $X$ be a continuous ra…

03:26

Payout on Insurance Polici…

05:56

Insurance Claims An insura…

02:14

An insurance company has d…

06:02

Find the expected value, t…

00:55

Insurance Sales The amount…

01:03

Verify that $f$ gives a jo…

in this question. We have a pdf great Ffx is equal to three by express to four when my ex is greater than equal to one. And I have zero when my ex is less than one on my excess less than one. Now what they're asking me is e want to find the expected value of the amount paid under the policy. So what is going to be the expected value off the amount paid? Now, the question is, an insurance company is issuing policy covering losses up to five. That is in thousands of dollars. Okay, so this is going to be for X greater than one, and this goes all the way up to five. All right, So what I have to do in this case is what is going to be the expected value? E is nothing but the integration rate is the integration off ex FF IX off eggs. Ffx dx. Right. So what I'm going to have to do is I'm going to have to integrate this function. So this is going to be from one all the way up to five. So what is my ffx f of X is going to be three by X rays to four into. I have eggs. This is an integration from 1 to 5. Or here I have DX. This is going to be X cubed. This becomes Excuse what? I can write this as three into X rays to minus three from 1 to 5. This is DX. Now, uh, the rule that I'm going to use the way is integral X rays to end. The X is equal to what? X rays to n plus one upon and plus one. This is what I'm going to use. So this becomes three comes outside as it is a constant. This becomes X rays to minus three plus one is what, minus two. So this becomes minus two upon minus two. This over here I have. This is one over here. This is a problem. It is five. Right. So this becomes minus three by two in 21 by X square. So this is one this is five. Okay, so this becomes minus three by two. Is as it is. Then I have mine. Then I have one by 25 minus one. So what does this make up? This pickups, minus 24 by 25 into three. By do. Right. So this is minus three by two. This is going to be into minus 24 by 25. So minus minus becomes plus, this becomes 12. 12 threes are 36 on 36 upon 25. If I pay attention, this is 36 divided by 25 1.44 So this is going to be my expected value in thousands of dollars. Of course, this is my answer.

View More Answers From This Book

Find Another Textbook

Insurance Reimbursement An insurance policy reimburses a loss up to a benefi…

Insurance An insurance policy pays for a random loss $X$ subject to a deduct…

Insurance An insurance policy costs $\$ 100$ and will pay policyholders $\$ …

Losses After Deductible A manufacturer's annual losses follow a distrib…

Insured Loss An insurance policy is written to cover a loss, $X$ where $X$ h…

Determine which are probability density functions and justify your answer.

Insured Loss An insurance policy is written to cover a loss, $X,$ where $X$ …

Suppose a homeowner spends $\$ 300$ for a home insurance policy that will pa…

The probability distribution for damage claims paid by the Newton Automobile…

Let $X$ be a continuous random variable with density function$$f(x)=\lef…

Let $X$ be a continuous random variable with density function$$f(x)=…

Payout on Insurance Policies An insurance company has written 100 policies f…

Insurance Claims An insurance company's monthly claims are modeled by a…

An insurance company has determined that in a certain region the probability…

Find the expected value, the variance, and the standard deviation, when they…

Insurance Sales The amount of insurance (in thousands of dollars) sold in a …

Verify that $f$ gives a joint probability density function. Then find the ex…

12:16

A Randstad/Harris interactive survey reported that 25$\%$ of employees said …

05:08

Suppose $X \sim \operatorname{Bin}(n, p),$ where the probability parameter $…

02:43

A sample of 50 Fortune 500 companies (Fortune, April $14,2003$ showed that 5…

08:10

It is often important in planning studies to know in advance what sample siz…

03:53

The Weibull distribution was introduced in Sect. $3.5 .$(a) Find the inv…

02:44

Suppose a simple random sample of size 50 is selected from a population with…

03:38

Individual A has a red die and $\mathrm{B}$ has a green die (both fair). If …

04:32

Exercise 109 of Chap. 1 referred to a multiple-choice exam in which 10 of th…

04:20

$$\begin{array}{l}{\text { Suppose that we have two events, } A \text { and …

03:57

For each of 18 preserved cores from oil-wet carbonate reservoirs, the amount…