menu
bartleby
search
close search
Hit Return to see all results
close solutoin list

Identifying Probability Density Functions In Exercises 25-30, use a graphing utility to graph the function. Then determine whether the function f represents a probability density function over the given interval. If f is not a probability density function, identify the condition(s) that is (are) not satisfied. f ( x ) = 1 14 , [ 1 , 14 ]

BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 26RE
Textbook Problem
3 views

Identifying Probability Density Functions In Exercises 25-30, use a graphing utility to graph the function. Then determine whether the function f represents a probability density function over the given interval. If f is not a probability density function, identify the condition(s) that is (are) not satisfied.

f ( x ) = 1 14 ,        [ 1 , 14 ]

To determine

To graph: The function f(x)=114 using a graphing utility and determine whether the function f(x)=114 represents a probability density function over the interval [1,14].

Explanation of Solution

Given Information:

The function f(x)=114 over the interval [1,14].

Graph:

Consider the provided function f(x)=114.

Use the ti-83 graphing calculator to construct the graph of the function.

Step 1: Open the ti-83 graphing calculator.

Step 2: Press [y=] and enter the function Y1=114.

Step 3: Press the [window] key and adjust the scale.

Xmin=0Xmax=14Xscl=1

And,

Ymin=0Ymax=214Yscl=0.01

Step 4: Press the [graph] key.

The bar graph of the function f(x)=114 is obtained as,

Consider the provided function f(x)=114 over the interval [1,14].

A function f of a continuous random variable x in the interval [a,b] is a probability density function if it is nonnegative and continuous on the interval [a,b].

And,

abf(x) dx=1

The provided function is a constant function and so the function f is continuous and nonnegative for all values on the interval [1,14].

Now, show that abf(x) dx=1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
Show all chapter solutions
add
Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 7-10, write the fraction as a...Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Random Selection In a class of 72 students, 44 are...Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Health The table shows the probability...Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Biology Consider a couple who have four children....Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Mean, Variance, and Standard Deviation In...Ch. 9.1 - Finding Mean, Variance, and Standard Deviation In...Ch. 9.1 - Revenue A publishing company introduces a new...Ch. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Baseball A baseball fan examined the record of a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Market Analysis A sporting goods company has...Ch. 9.1 - Market Analysis Repeat Exercise 37 for the case in...Ch. 9.2 - Show that f(x)=12x is a probability density...Ch. 9.2 - Show that f(x)=2e2x is a probability density...Ch. 9.2 - Find the probability that x lies in the interval...Ch. 9.2 - A probability density function is defined over the...Ch. 9.2 - For the function in Example 5. find the...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability A probability density...Ch. 9.2 - Finding a Probability A probability density...Ch. 9.2 - Waiting Time Buses arrive and depart from a...Ch. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Learning Theory The time t (in hours) required for...Ch. 9.2 - HOW DO YOU SEE IT? The graph shows two models for...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Meteorology A meteorologist predicts that the...Ch. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Demand Using the probability density function in...Ch. 9.3 - Find the expected value of the probability density...Ch. 9.3 - Find the variance and standard deviation of the...Ch. 9.3 - Use a symbolic integration utility to find the...Ch. 9.3 - Find the mean and median of the probability...Ch. 9.3 - Find the expected value and standard deviation of...Ch. 9.3 - Find the probability that a person selected at...Ch. 9.3 - Checkpoint 7 Worked-out solution available at...Ch. 9.3 - In Exercises 1 and 2, use integration by parts to...Ch. 9.3 - In Exercises 1 and 2, use integration by parts to...Ch. 9.3 - In Exercises 3 and 4, evaluate the definite...Ch. 9.3 - In Exercises 3 and 4, evaluate the definite...Ch. 9.3 - In Exercises 5 and 6, find each probability using...Ch. 9.3 - In Exercises 5 and 6, find each probability using...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using two Methods In Exercises 1316, find the...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Finding Probabilities In Exercises 35 and 36, let...Ch. 9.3 - Finding Probabilities In Exercises 35 and 36, let...Ch. 9.3 - Consumer Trends The number of coupons x used by a...Ch. 9.3 - Cost The daily cost x (in dollars) of electricity...Ch. 9.3 - Useful Life The useful lifetime of a product is...Ch. 9.3 - Useful Life The useful lifetime of a product is...Ch. 9.3 - Transportation The arrival time t (in minutes) of...Ch. 9.3 - Transportation Repeat Exercise 41 for a bus that...Ch. 9.3 - Useful Life The time t (in years) until failure of...Ch. 9.3 - Useful Life The time t (in years) until failure of...Ch. 9.3 - Waiting Time The waiting time t (in minutes) for...Ch. 9.3 - License Renewal The waiting time t (in minutes) at...Ch. 9.3 - Demand The daily demand x for a certain product...Ch. 9.3 - Demand Repeat Exercise 47 for the probability...Ch. 9.3 - Demand The daily demand x for water (in millions...Ch. 9.3 - HOW DO YOU SEE IT? In chemistry, the probability...Ch. 9.3 - Wages The employees of a large corporation are...Ch. 9.3 - Medical Science A medical research team has...Ch. 9.3 - Education For high school graduates from 2012...Ch. 9.3 - Fuel Mileage Assume the fuel mileages of all 2015...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Frequency Distributions In Exercises 5 and 6,...Ch. 9 - Frequency Distributions In Exercises 5 and 6,...Ch. 9 - Bar Code Use the frequency distribution in...Ch. 9 - Kittens Use the frequency distribution in Exercise...Ch. 9 - Identifying Probability Distributions In Exercises...Ch. 9 - Identifying Probability Distributions In Exercises...Ch. 9 - Using Probability Distributions In Exercises 11...Ch. 9 - Using Probability Distributions In Exercises 11...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Revenue A publishing company introduces a new...Ch. 9 - Raffle A service organization is selling $5 raffle...Ch. 9 - Consumer Trends The probability distribution of...Ch. 9 - Vital Statistics The probability distribution of...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Medicine The time t (in days) until recovery after...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Transportation The arrival time t (in minutes) of...Ch. 9 - Transportation Repeat Exercise 55 for a train that...Ch. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Useful Life The time t (in hours) until failure of...Ch. 9 - Demand The daily demand x for a certain product...Ch. 9 - Demand Repeat Exercise 59 for the probability...Ch. 9 - Education In 2013, the scores on the Medical...Ch. 9 - Botany In a botany experiment, plants are grown in...Ch. 9 - Four students answer a true-false question on an...Ch. 9 - A card is chosen at random from a standard 52-card...Ch. 9 - In Exercises 3 and 4, sketch a graph of the...Ch. 9 - In Exercises 3 and 4, sketch a graph of the...Ch. 9 - In Exercises 5 and 6, find the expected value,...Ch. 9 - In Exercises 5 and 6, find the expected value,...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - An intelligence quotient or IQ is a number that is...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions add
Simplify Simplify the rational expression. 19. x2+5x+6x2+8x+15

Precalculus: Mathematics for Calculus (Standalone Book)

Describe the set of points (x,y) such that x2+y2=0.

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 5-8, plot the graph of the function f in an appropriate viewing window. (Note: The answer is not u...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Explain the difference between simple interest and compound interest.

Finite Mathematics for the Managerial, Life, and Social Sciences

0 1 −∞ does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find for defined implicity by .

Study Guide for Stewart's Multivariable Calculus, 8th

Evaluate each sum. k=34(2k2)

College Algebra (MindTap Course List)