/*! 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. 5.25 Let Y=X-饾湀饾浖.Show that if X ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.25 (page 216)

Let Y=X-饾湀饾浖.

Show that if X is a Weibull random variable with parameters 谓, 伪, and 尾, then Y is an exponential random variable with parameter 位 = 1 and vice versa.

Short Answer

Expert verified

The above statement is proved.

Step by step solution

01

Given information

We are assuming thatXis a Weibull with parameters饾湀,饾浖and饾浗

02

Calculation

We have

PX-饾湀饾浖饾浗鈮�x=PX-饾湀饾浖鈮�x1饾浗=PX鈮�饾湀+饾浖x1饾浗=1-e-x

which is nothing but the CDF of exponential distribution.

Therefore it's proved that Ywill follow exponential distribution with parameter饾浑=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

The median of a continuous random variable having distribution function F is that value m such that F(m) = 12. That is, a random variable is just as likely to be larger than its median as it is to be smaller. Find the median of X if X is

(a) uniformly distributed over (a, b);

(b) normal with parameters 渭,蟽2;

(c) exponential with rate 位.

Let Xbe a random variable with probability density function

f(x)=c(1-x2)鈭�1<x<10otherwise

(a) What is the value of c?

(b) What is the cumulative distribution function of X?

The density function of Xis given by

role="math" localid="1646816210505" f(x)=a+bx2;0鈮�x鈮�10;Otherwise

Ifrole="math" localid="1646816286362" EX=35, findaandb.

With 桅(x)being the probability that a normal random variable with mean 0and variance 1is less than x, which of the following are true:

(a)桅(-x)=桅(x)

(b)桅(x)+桅(-x)=1

(c)桅(-x)=1/桅(x)

A randomly chosen IQtest taker obtains a score that is approximately a normal random variable with mean 100and standard deviation 15. What is the probability that the score of such a person is

(a) more than 125;

(b) between 90and 110?

See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.