/*! 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} 7.11 Suppose in Self-Test Problem 7.3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: 7.11 (page 364)

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.

Short Answer

Expert verified

The expected value of the number of married couples that are seated at the same table is2219.

Step by step solution

01

Given Information

20people are to be seated at seven tables, three of which have 4seats and four of which have 2seats.

02

Explanation

Indicator variables as,

whereby,

Ej,j=1,2,鈥�,10denotes the events.

E_j="jth married couple is at the same table.

Then, X=鈭�j=110Ij.

and therefore the expected number of married couples that are seated at the same table is

E[X]=E鈭�j=110Ij=鈭�j=110EIj=鈭�j=110PEj路(*)

03

Explanation

Consider the next events,

Wji="woman from jth married couple is ati th table " ,

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

Let X1,鈥�,Xnbe independent and identically distributed continuous random variables. We say that a record value occurs at time j,j鈮�n,if Xj鈮�Xlfor all 1鈮�i鈮�j. Show that

(a) E[number of record values]=鈭�j=1n1/j

(b) Var鈦�(number of record values)=鈭�j=1n鈥�(j鈭�1)/j2

Let X1,X2,鈥�,Xnbe independent random variables having an unknown continuous distribution function Fand let Y1,Y2,鈥�,Ymbe independent random variables having an unknown continuous distribution function G. Now order those n+mvariables, and let

Ii=1鈥呪赌呪赌呪赌�if theith smallest of then+m鈥呪赌呪赌呪赌�variables is from theXsample0鈥呪赌呪赌呪赌�otherwise

The random variable R=鈭�i=1n+miIiis the sum of the ranks of the Xsample and is the basis of a standard statistical procedure (called the Wilcoxon sum-of-ranks test) for testing whether Fand Gare identical distributions. This test accepts the hypothesis that F=Gwhen Ris neither too large nor too small. Assuming that the hypothesis of equality is in fact correct, compute the mean and variance of R.

Hint: Use the results of Example 3e.

A coin having probability p of landing on heads is flipped n times. Compute the expected number of runs of heads of size 1 , of size 2 , and of size k,1鈮�k鈮�n.

Let Z be a standard normal random variable,and, for a 铿亁ed x, set

X={ZifZ>x0otherwise

Show thatE[X]=12蟺e鈭�x2/2.

Successive weekly sales, in units of 1,000, have a bivariate normal distribution with common mean 40, common standard deviation 6, and correlation .6.

(a) Find the probability that the total of the next 2 weeks鈥� sales exceeds 90.

(b) If the correlation were .2rather than .6, do you think that this would increase or decrease the answer to (a)? Explain your reasoning.

(c) Repeat (a) when the correlation is 2.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.