/*! 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.7.39 Let X1,聽.聽.聽.be independent w... [FREE SOLUTION] | 魅影直播

魅影直播

Log out

Learning Materials

Features

Discover

Chapter 7: Q.7.39 (page 355)

Let X1,...be independent with common mean 渭and common variance 蟽2, and set Yn=Xn+Xn+1+Xn+2. For j鈮�0, find CovYn,Yn+j.

Short Answer

Expert verified

The value ofCovYn,Yn+jis0.

Step by step solution

01

Given Information

Independent variable =X1

Mean =渭

Common variance =蟽2

Set functionYn=Xn+Xn+1+Xn+2

For j鈮�0, findCovYn,Yn+j

02

Explanation

From the information, observe that X1,鈥�..be independent with common mean 渭and common variance 蟽2

we have that,

CovYn,Yn=VarXn+Xn+1+Xn+2

=VarXn+VarXn+1+VarXn+2

=蟽2+蟽2+蟽2

=3蟽2

Due to the variance of sum of nindependent variables with common distribution

03

Explanation

If j=1, we have that

CovYn,Yn+1=CovXn+Xn+1+Xn+2,Xn+1+Xn+2+Xn+3

=VarXn+1+VarXn+2

=蟽2+蟽2

=2蟽2

If j=2,we have that,

CovYn,Yn+2=CovXn+Xn+1+Xn+2,Xn+2+Xn+3+Xn+4

=VarXn+2

=蟽2

For j鈮�3,we see that, CovYn,Yn+j=0

Since the definition of Ynand basic properties of covariance to obtain the required.

04

Final Answer

Hence, the value ofCovYn,Yn+jis0.

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 魅影直播!

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 a gambler who, at each gamble, either wins or loses her bet with respective probabilities pand 1-p. A popular gambling system known as the Kelley strategy is to always bet the fraction 2p-1of your current fortune when p>12. Compute the expected fortune afterngambles of a gambler who starts with xunits and employs the Kelley strategy.

A certain region is inhabited by r distinct types of a certain species of insect. Each insect caught will, independently of the types of the previous catches, be of type i with probability

Pi,i=1,鈥�,r鈭�1rPi=1

(a) Compute the mean number of insects that are caught before the 铿乺st type 1catch.

(b) Compute the mean number of types of insects that are caught before the 铿乺st type1 catch.

Let X1,X2,鈥�,Xn be independent and identically distributed positive random variables. For k鈮�n findE鈭�i=1kXi鈭�i=1nXi.

The number of people who enter an elevator on the ground floor is a Poisson random variable with mean 10. If there are N floors above the ground floor, and if each person is equally likely to get off at any one of theN floors, independently of where the others get off, compute the expected number of stops that the elevator will make before discharging all of its passengers.

Suppose in Self-Test Problem 7.3that the 20people are to be seated at seven tables, three of which have 4seats and four of which have 2seats. If the people are randomly seated, find the expected value of the number of married couples that are seated at the same table.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

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.