/*! 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} Q9E An individual named Claudius is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q9E (page 99)

An individual named Claudius is located at the point 0 in the accompanying diagram. Using an appropriate randomization device (such as a
tetrahedral die, one having four sides), Claudius first moves to one of the four locations B1, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin.

a. Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X? Is X discrete or continuous?

b. If moves are allowed also along the diagonal paths connecting 0 to A1, A2, A3, and A4, respectively, answer the questions in part (a).

Short Answer

Expert verified

a. The possible values of X are\(X = \left\{ {2,4,6, \ldots } \right\}\). Discrete

b. The possible values of X are\(X = \left\{ {2,3,4,5, \ldots } \right\}\). Discrete

Step by step solution

01

Given information

There is a person called Claudius located at the point zero and the experiment is performed in which he has to move to any of the four location B1, B2, B3 and B4, and the next move is either return to zero or move to other two adjacent point is observed.

02

Determine the possible values of random variable X

a.

Let us suppose Claudius make the second move and return to zero then this the minimum number of moves that Claudius make before returning to zero is two.

If in the second move he moves to any of the other two adjacent points then he has to make two more moves before returning to zero is 4.

In continuation to the above possible values of Xis given as,

\(X = \left\{ {2,4,6, \ldots } \right\}\)

As the possible values of X is countable and finite then this is the discrete random variable.

03

Determine the possible values of X when moves are also allowed along the diagonal paths

b.

In this case if moves are allowed diagonally then the third move is either return to point zero or move to other adjacent points.

Claudius from its location at point zero initially make his first move to any of the four locations B1, B2, B3 and B4 then make the second move and return to zero then this the minimum number of movies that Claudius make before returning to zero is two.

If in the second move he moves to any of the other two adjacent points, then he has to make another move either returning to point 0 or move to other adjacent points.

If he makes a move to return to 0 then the number of moves will be 3.

If he makes a move to return in his fourth move then the total number of moves will be 5.

In continuation to the above possible values of X is given as,

\(X = \left\{ {2,3,4,5, \ldots } \right\}\)

As the possible values of X is countable and finite then this is the discrete random variable.

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

Who studies more? Researchers asked the students in a large first-year college class how many minutes they studied on a typical weeknight. The back-to-back stemplot displays the responses from random samples of 30women and 30 men from the class, rounded to the nearest 10minutes. Write a few sentences comparing the male and female distributions of study time.

The article 'should You Report That Fender Bender?" (Consumer Reports, Sept. 2013: 15) reported that 7 in 10 auto accidents involve a single vehicle (the article recommended always reporting to the insurance company an accident involving multiple vehicles). Suppose 15 accidents are randomly selected. Use Appendix Table A.l to answer each of the following questions.

a. What is the probability that at most 4 involve a single vehicle?

b. What is the probability that exactly 4 involve a single vehicle?

c. What is the probability that exactly 6 involve multiple vehicles?

d. What is the probability that between 2 and 4 , inclusive, involve a single vehicle?

e. What is the probability that at least 2 involve a single vehicle?

f. What is the probability that exactly 4 involve a single vehicle and the other 11 involve multiple vehicles?

The Center for Disease Control and Prevention reported in\(2012\)that\(1\)in\(88\)American children had been diagnosed with an autism spectrum disorder (ASD).

a. If a random sample of\(200\)American children is selected, what are the expected value and standard deviation of the number who have been diagnosed with ASD?

b. Referring back to (a), calculate the approximate probability that at least\(2\)children in the sample have been diagnosed with ASD?

c. If the sample size is\(352\), what is the approximate probability that fewer than\(5\)of the selected children have been diagnosed with ASD?

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A)\({\rm{ = }}{\rm{.5}}\), P(B)\({\rm{ = }}{\rm{.2}}\), and P(C)\({\rm{ = }}{\rm{.3}}\). a. Among the next\({\rm{100}}\)customers, what are the mean and variance of the number who pay with a debit card? Explain your reasoning. b. Answer part (a) for the number among the\({\rm{100}}\)who don鈥檛 pay with cash.

The mode of a discrete random variable \({\rm{X}}\) with \({\rm{pmf}}\) \({\rm{p(x)}}\) is that value \({{\rm{x}}^{\rm{*}}}\) for which \({\rm{p(x)}}\) is largest (the most probable \({\rm{x}}\) value).

a. Let \({\rm{X}} \sim {\rm{Bin(n,p)}}\). By considering the ratio \({\rm{b(x + 1;n,p)/b(x;n,p)}}\), show that \({\rm{b(x;n,p)}}\) increases with x as long as \({\rm{x < np - (1 - p)}}\). Conclude that the mode \({{\rm{x}}^{\rm{*}}}\) is the integer satisfying \({\rm{1}} \le {{\rm{x}}^{\rm{*}}} \le {\rm{(n + 1)p}}\).

b. Show that if \({\rm{X}}\) has a Poisson distribution with parameter \({\rm{\mu }}\), the mode is the largest integer less than \({\rm{\mu }}\). If \({\rm{\mu }}\) is an integer, show that both \({\rm{\mu - 1}}\) and \({\rm{\mu }}\) are modes.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.