Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q.2 (page 409)

Suppose that three randomly selected subjects solve puzzles for five minutes each. The expected value of the total number of puzzles solved by the three subjects is

(a) 1.8. (c) 2.5. (e)7.5.

(b) 2.3. (d) 6.9.

Short Answer

Expert verified

Expected value of total number of puzzle is 6.9

Step by step solution

01

Given information

Given in the question that, Suppose that three randomly selected subjects solve puzzles for five minutes each. We need to find the expected value of the total number of puzzles solved by the three subjects.

02

Explanation

The expected value can be calculated by adding the product of each conceivable event and its probability of occurrence.

μX=∑xP(x)=1×0.2+2×0.4+3×0.3+4×0.1=2.3

μ3X=3μX=3(2.3)=6.9

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 you roll a pair of fair, six-sided dice until you get doubles. Let T=the number of rolls it takes.

Find P(T=3). Interpret this result in context.

For each of the following situations, determine whether the given random variable has a binomial distribution. Justify your answer.

Choose three students at random from your class. Let Y=the number who are over 6feet tall.

Benford’s law and fraud Refer to Exercise 13. It might also be possible to detect an employee’s fake expense records by looking at the variability in the first digits of those expense amounts.

(a) Calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.

(b) Now calculate the standard deviation of first digits that follow Benford’s law (Exercise 5). Would using standard deviations be a good way to detect fraud? Explain.

Life insurance A life insurance company sells a term insurance policy to a21-year-old male that pays 100,000if the insured dies within the next 5years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of 250each year as payment for the insurance. The amount Y that the company earns on this policy is 250per year, less the 100,000that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of Y=profit earned by the company:

(a) Copy the table onto your paper. Fill in the missing values of Y.

(b) Find the missing probability. Show your work.

(c) Calculate the mean μY. Interpret this value in context.

How well does it fit? (3.2) Discuss what s, r2, and the residual plot tells you about this linear regression model.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.

Sign-up for free