/*! 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.7.3 If X聽and Y are independent and ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q.7.3 (page 354)

If Xand Y are independent and identically distributed with mean 渭and variance 蟽2, find

E(X鈭�Y)2

Short Answer

Expert verified

The value of E(X鈭�Y)2is

E(X鈭�Y)2=2蟽2

Step by step solution

01

Step 1:Given Information

XandYare autonomous and identically allocated with mean渭and variance 蟽2.

02

Step 2:Explanation

E[X]=E[Y]=渭

Var(X)=Var(Y)=蟽2

Var(X)=EX2鈭�(E[X])2

EX2=Var(X)+(E[X])2

=蟽2+渭2

X and Y are independent,

E(X鈭�Y)2=EX2鈭�2XY+Y2

=EX2鈭�2E[X]E[Y]+EY2

=蟽2+渭2鈭�2渭渭+蟽2+渭2

=2蟽2+2渭2鈭�2渭2

=2蟽2

03

Step 3:Final Answer

E(X鈭�Y)2=2蟽2

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

A group of 20 people consisting of 10 men and 10 women is randomly arranged into 10 pairs of 2 each. Compute the expectation and variance of the number of pairs that consist of a man and a woman. Now suppose the 20 people consist of 10 married couples. Compute the mean and variance of the number of married couples that are paired together.

Show how to compute Cov(X,Y) from the joint moment generating function ofX and Y.

Let X1,X2,鈥�be a sequence of independent and identically distributed continuous random variables. Let N鈮�2be such that

X1鈮�X2鈮�鈰�鈮�XN-1<XN

That is, Nis the point at which the sequence stops decreasing. Show that E[N]=e.

Hint: First find P{N鈮�n}.

The joint density of Xand Yis given by

f(x,y)=e-yy,0<x<y,0<y<鈭�

Compute EX3鈭�Y=y.

Suppose that A and B each randomly and independently choose3of10objects. Find the expected number of objects

a. Chosen by both A and B;

b. Not chosen by either A or B;

c. Chosen by exactly one of A and B.

See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

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.