/*! 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.6.10 The joint probability density fu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q.6.10 (page 275)

The joint probability density function of X and Y is given by f(x, y) = e-(x+y) 0 鈥� x < q, 0 鈥� y < q Find

(a) P{X < Y} and

(b) P{X < a}.

Short Answer

Expert verified

a. P{X<Y}=12

b.P{X<a}=1-e-a

Step by step solution

01

Content Introduction

The likelihood of an occasion is the extent of times the occasion occurs out of an enormous number of preliminaries.

02

Explanation (Part a)

Observe that their joint density function can be factorized as:

f(x,y)=e-(x+y)=e-xe-y=fX(x)fY(y)

So because X and Y are equally distributed random variables with distribution Expo(1) and they are independent since the joint density function can be factorized. Because of the equal distribution, we have that

P(X<Y)=12

03

Explanation (part b)

Use the fact that X~Expo(1)to obtain that

P(X<a)=P(X鈮�a)=FX(a)=1-e-afora鈮�0, otherwise it is equal to zero.

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

Verify Equation 1.2.P(a1<X鈮�a2,b1<Y鈮�b2)=F(a2,b2)+F(a1,b1)鈭�F(a1,b2)鈭�F(a2,b1)

6. Let X and Y be continuous random variables with joint density function f(x,y)=x5+cy鈥呪赌呪赌呪赌�0<x<1,1<y<50鈥呪赌呪赌呪赌�otherwise

where c is a constant.

(a) What is the value of c?

(b) Are X and Y independent?

(c) FindP[X+Y>3]

A television store owner figures that 45 percent of the customers entering his store will purchase an ordinary television set, 15 percent will purchase a plasma television set, and 40 percent will just be browsing. If 5 customers enter his store on a given day, what is the probability that he will sell exactly 2 ordinary sets and 1 plasma set on that day?

Suppose that the number of events occurring in a given time period is a Poisson random variable with parameter 位. If each event is classified as a type ievent with probabilitypi,i=1,....,n,鈭�pi=1, independently of other events, show that the numbers of type ievents that occur,i=1,....,n, are independent Poisson random variables with respective parameters位pi,i=1,.....,n.

Derive the distribution of the range of a sample of size 2 from a distribution having density function f(x)=2x,0<x<1.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Discrete 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.