Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q 5.137. (page 230)

Dice. The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows

Part (a) Find and interpret the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10

Part (c) Construct a probability histogram for the random variable, locate the mean: and show one, two, and three standard deviation intervals.

Short Answer

Expert verified

Part (a) 7

Part (b) 2.42

Part (c)

Step by step solution

01

Part (a) Step 1. Given information. 

Consider the following table of data. When two Balanced dice are rolled, the random variable Y is the sum of the dice.

02

Part (a) Step 2. The random variable's average.

μ=∑y·P(Y=y)μ=21/36+3(1/18)+......121/36μ=0+0.056+0.167+.....0.333μ=7

Two balanced dice are rolled, the mean of the sum of the dice is 7

03

Part (b) Step 1.The random variable's standard deviation:

Standard deviation

σ=∑x2P(X=x)-μ2σ=41/36+91/18.....1441/36-72σ=5.833σ=2.415

As a result, standard deviation = 2.42

04

Part (c) Step 1.  The mean, one, two, and three standard deviation intervals on the probability histogram graph of the random variable.

We have μand σfrom sections a and b.

μ-σ,μ+σ=7-2.42,7+2.42=4.58,9.41μ-2σ,μ+2σ=7-2(2.42),7+2(2.42)=(2.17,11.83)μ-3σ,μ+3σ=7-3(2.42),7+3(2.42)=(-0.25,14.25)

Draw the probability histogram graph:

The probability histogram graph of the random variable with the mean and one, two, and three standard deviation intervals is shown above.

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

The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money?

Die and coin. Consider the following random experiment : First , roll a die and observe the number of dots facing up: then toss a coin the number of times that the die shows and observe the total number of heads. Thus , if the die shows three dots facing up and the coin (which is then tossed tree times) comes up heads exactly twice, then the outcome of the experiment can be represent as (3,2).

Part (a) Determine a sample space for this experiment.

Part (b) Determine the events that the total number of heads is even.

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

n=6,p=0.5,P(X=4)

A bowl contains 12 poker chips 3 red , 4 white and 5 blue. One of these poker chips is selected at random from the bowl. Let B denote the event that the chips is selected is blue. Find the probability that a blue chips is selected, and express your answer in probability notation

For each of the following probability histograms of binomial distributions, specify whether the success probability is less than, equal to, or greater than 0.5. Explain your answers.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.

Sign-up for free