/*! 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.4.6 In Problem 4.5,for n=3,if the co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q.4.6 (page 163)

In Problem 4.5,for n=3,if the coin is assumed fair, what are the probabilities associated with the values that X can take on?

Short Answer

Expert verified

For n=3,

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

Step by step solution

01

Step1: Given Information

X - It is the difference between the number of heads and the number of tails.

02

Step2: Explanation

Possible outcomes of X, when a coin is tossed n times are:

If the number of tails is t, then the number of heads(h) is n-t.

h=n-t

Therefore X can be written as:

X=h-t=n-t-t=n-2t

Therefore possible outcomes of X are:

{n-2t鈭�t鈭�{0,1,鈥�,n}}

Here localid="1646472975417" n=3,

The result is {3-2t鈭�t鈭�{0,1,2,3}}

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

03

Step3: Final Result

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

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

An urn initially contains one red and one blue ball. At each stage, a ball is randomly chosen and then replaced along with another of the same color. Let X denote the selection number of the 铿乺st chosen ball that is blue. For instance, if the 铿乺st selection is red and the second blue, then X is equal to 2.

  • (a) Find P{X>i},i鈮�1
  • (b) Show that with probabilityrole="math" 1, a blue ball is eventually chosen. (That is, show thatP{X<鈭�}=1.)
  • (c) FindE[X].

Let Xbe a negative binomial random variable with parameters rand p, and let Ybe a binomial random variable with parameters nand p. Show that

P{X>n}=P{Y<r}

Hint: Either one could attempt an analytical proof of the preceding equation, which is equivalent to proving the identity

鈭�i=n+1鈭�鈥�i鈭�1r鈭�1pr(1鈭�p)i鈭�r=鈭�i=0r鈭�1鈥�ni脳pi(1鈭�p)ni

or one could attempt a proof that uses the probabilistic interpretation of these random variables. That is, in the latter case, start by considering a sequence of independent trials having a common probability p of success. Then try to express the events to express the events {X>n}and {Y<r}in terms of the outcomes of this sequence.

In Example 8i, what percentage of idefective lots does the purchaser reject? Find it fori=1,4.Given that a lot is rejected, what is the conditional probability that it contained 4defective components?

The National Basketball Association (NBA) draft lottery involves the 11 teams that had the worst won-lost records during the year. A total of 66 balls are placed in an urn. Each of these balls is inscribed with the name of a team: Eleven have the name of the team with the worst record, 10 have the name of the team with the second worst record, 9 have the name of the team with the third worst record, and so on (with 1 ball having the name of the team with the 11 th-worst record). A ball is then chosen at random, and the team whose name is on the ball is given the first pick in the draft of players about to enter the league. Another ball is then chosen, and if it "belongs" to a team different from the one that received the first draft pick, then the team to which it belongs receives the second draft pick. (If the ball belongs to the team receiving the first pick, then it is discarded and another one is chosen; this continues until the ball of another team is chosen.) Finally, another ball is chosen, and the team named on the ball (provided that it is different from the previous two teams) receives the third draft pick. The remaining draft picks 4 through 11 are then awarded to the 8 teams that did not "win the lottery," in inverse order of their won-lost not receive any of the 3 lottery picks, then that team would receive the fourth draft pick. Let X denote the draft pick of the team with the worst record. Find the probability mass function of X.

Suppose that the distribution function of X given by

F(b)=0鈥呪赌呪赌呪赌�b<0b4鈥呪赌呪赌呪赌�0鈮�b<112+b鈭�14鈥呪赌呪赌呪赌�1鈮�b<21112鈥呪赌呪赌呪赌�2鈮�b<31鈥呪赌呪赌呪赌�3鈮�b

(a) Find P{X=i},i=1,2,3.

(b) Find P12<X<32.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure 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.