/*! 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. 8.17 Redo Example5b聽under the assump... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q. 8.17 (page 391)

Redo Example5bunder the assumption that the number of man-woman pairs is (approximately) normally distributed. Does this seem like a reasonable supposition?

Short Answer

Expert verified

Therefore,

P{X鈮�30}鈮�0.

Step by step solution

01

Given Information.

the number of man-woman pairs is (approximately) normally distributed.

02

Explanation.

Consider Example5b(textbook). Now, assume that the number of man-woman pairs

X=鈭�i=1100Xi,whereXi=1,maniis paired with a woman0,otherwise

is approximately normally distributed with a meanE[X]鈮�50.25and a variance Var(X)鈮�25.126

The probability that most 30pairs will consist of a man and a woman isP{X鈮�30}. To approximate this probability we can use the central limit theorem and in that case, we get:

localid="1649832005870" P{X鈮�30}鈮�PX-E[X]Var(X)鈮�30-E[X]Var(X)localid="1649831889184" =PX-50.2525.126鈮�30-50.2525.126

鈮�0.

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

Suppose that a fair die is rolled 100times. Let Xibe the value obtained on the ith roll. Compute an approximation forP鈭�1100Xi鈮�a1001<a<6.

(a)Let Xbe a discrete random variable whose possible values are1,2,.... If P[X=k]is nonincreasingk=1,2,..., prove that

P(X=k)鈮�2E[X]k2

(b)Let Xbe a non-negative continuous random variable having a nonincreasing density function. Show thatf(x)鈮�2E[X]x2for allx>0.

Let f(x)be a continuous function defined for0鈮�x鈮�1. Consider the functions

Bn(x)=鈭�k=0nfknnkxk(1鈭�x)n-k(called Bernstein polynomials) and prove that

limn鈫�鈭�Bn(x)=f(x).

Hint: Let X1,X2,...be independent Bernoulli random variables with meanx. Show that

Bn(x)=Efx1+...+xnn

and then use Theoretical Exercise8.4.

Since it can be shown that the convergence of Bn(x)to f(x)is uniformx, the preceding reasoning provides a probabilistic proof of the famous Weierstrass theorem of analysis, which states that any continuous function on a closed interval can be approximated arbitrarily closely by a polynomial.

In Problem8.7, suppose that it takes a random time, uniformly distributed over(0,.5), to replace a failed bulb. Approximate the probability that all bulbs have failed by time550.

Many people believe that the daily change in the price of a company鈥檚 stock on the stock market is a random variable with a mean of 0and a variance of蟽2. That is if Yn represents the price of the stock on thenth day, then Yn=Yn-1+Xn,n鈮�1where X1,X2,...are independent and identically distributed random variables with mean 0and variance蟽2. Suppose that the stock鈥檚 price today is100. If蟽2=1, what can you say about the probability that the stock鈥檚 price will exceed 105after10days?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.