/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 5.27 If x聽is uniformly distributed o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.27 (page 216)

If xis uniformly distributed over (a,b), what random variable, having a linear relation with x, is uniformly distributed over (0,1)?

Short Answer

Expert verified

Random variable having linear relation withxisY=X-ab-a

Step by step solution

01

Random variable

Given that X~Unif(a,b).

Approach Random variable

Y=X-ab-a

02

Explanation

SinceX鈭�(a,b).

Y鈭�(0,1).

For y鈭�(0,1),

P(Y鈮�y)=PX-ab-a鈮�y

=P(X鈮�a+(b-a)y)

=a+(b-a)y-ab-a

=y

Proved that Y~Unif(0,1).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Consider the function

f(x)=C(2x鈭�x3)0<x<520otherwise

Could fbe a probability density function? If so, determine

C. Repeat if f(x)were given by

localid="1646632841793" f(x)=C(2x鈭�x3)0<x<520otherwise

Let Xbe a random variable that takes on values between0andc. That isP0鈮�X鈮�c=1.Show that

Var(X)鈮�c24

Hint: One approach is to first argue that

localid="1646883602992" EX2鈮�cEX

and then use this inequality to show that

Var(X)鈮�c2[伪(1-伪)]where伪=E[X]c

A system consisting of one original unit plus a spare

can function for a random amount of timeX. If the density

ofXis given (in units of months) by

f(x)=Cxe-x/2x>00x鈮�0

what is the probability that the system functions for at least 5months?

Compute the hazard rate function of a gamma random variable with parameters (伪,位)and show it is increasing when 伪鈮�1and decreasing when 伪鈮�1

Verify thatVar(X)=伪位2whenXis a gamma random variable with parameters 伪and 位
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.