Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 3: Q20E (page 117)

In Exercise 13 of Sec. 3.2, draw a sketch of the c.d.f. F(x)of X and findF (10)

Short Answer

Expert verified

The value F (10) is 0.225

Step by step solution

01

Drawing the graph for the cdf F(x)  

Steps to draw the graph

  1. Taking random variable X on x-axis with the range of 5
  2. Take the cdf F (x) on y-axis with range 0.02
  3. From exercise 13 of sec 3.2 the cdf is equal to 0.0045x2/2 for 0<x<20
  4. Plot the graph for the x vs F (x)

02

Calculating the value of F(10) 

From the given graph of cdf and random variable.

The value of F(10) =0.225

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question:Suppose thatXandYhave a discrete joint distributionfor which the joint p.f. is defined as follows:

\({\bf{f}}\left( {{\bf{x,y}}} \right){\bf{ = }}\left\{ \begin{array}{l}\frac{{\bf{1}}}{{{\bf{30}}}}\left( {{\bf{x + y}}} \right)\;{\bf{for}}\;{\bf{x = 0,1,2}}\;{\bf{and}}\;{\bf{y = 0,1,2,3}}\\{\bf{0}}\;{\bf{otherwise}}\end{array} \right.\)

a. Determine the marginal p.f.’s ofXandY.

b. AreXandYindependent?

Suppose that a random variableXhas the binomial distribution

with parametersn=8 andp=0.7. Find Pr(X≥5)by using the table given at the end of this book. Hint: Use the fact that Pr(X≥5)=Pr(Y≤3), whereYhas thebinomial distribution with parametersn=8 andp=0.3.

Suppose that thenrandom variablesX1. . . , Xnform arandom sample from a discrete distribution for which thep.f. is f. Determine the value of Pr(X1 = X2 = . . .= Xn).

Suppose that a random variableXhas the binomial distribution with parametersn=15 andp=0.5. Find Pr(X <6).

An insurance agent sells a policy that has a \(100 deductible

and a \)5000 cap. When the policyholder files a claim, the policyholder must pay the first \(100. After the first \)100, the insurance company pays therest of the claim up to a maximum payment of $5000. Any

excess must be paid by the policyholder. Suppose that thedollar amount X of a claim has a continuous distribution

with p.d.f. \({\bf{f}}\left( {\bf{x}} \right){\bf{ = }}\frac{{\bf{1}}}{{{{\left( {{\bf{1 + x}}} \right)}^{\bf{2}}}}}\) for x>0 and 0 otherwise.

LetY be the insurance company's amount to payon the claim.

a. Write Y as a function of X, i.e., \({\bf{Y = r}}\left( {\bf{X}} \right).\)

b. Find the c.d.f. of Y.

c. Explain why Y has neither a continuous nor a discretedistribution.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free