   # Finding a Probability In Exercises 31-36, sketch the graph of the probability density function over the indicated interval and find each probability. f ( x ) = 2 ( x + 1 ) 2 , [ 0 , 1 ] (a) P ( 0 &lt; x &lt; 1 2 ) (b) P ( 1 4 &lt; x &lt; 3 4 ) (c) P ( x ≥ 1 2 ) (d) P ( 1 10 &lt; x &lt; 3 10 ) ### Calculus: An Applied Approach (Min...

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

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 35RE
Textbook Problem
1 views

## Finding a Probability In Exercises 31-36, sketch the graph of the probability density function over the indicated interval and find each probability. f ( x ) = 2 ( x + 1 ) 2 , [ 0 , 1 ] (a) P ( 0 < x < 1 2 ) (b) P ( 1 4 < x < 3 4 ) (c) P ( x ≥ 1 2 ) (d) P ( 1 10 < x < 3 10 )

To determine

To graph: The probability density function f(x)=2(x+1)2 over the interval [0,1] and calculate the probabilities (a) P(0<x<12) (b) P(14<x<34), (c) P(x12),(d) P(110<x<310).

### Explanation of Solution

Given Information:

The probability density function f(x)=2(x+1)2 over the interval [0,1].

Graph:

Consider the provided probability density function.

f(x)=2(x+1)2

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=2(x+1)2.

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

Xmin=0Xmax=1Xscl=0.1

And

Ymin=0Ymax=2Yscl=0.1

Step 4: Press the [GRAPH] key.

The graph of the function f(x)=2(x+1)2 is obtained as,

Now, calculate the probabilities.

Consider the provided probability density function f(x)=2(x+1)2.

Use the formula P(cxd)=cdf(x) dx to calculate the required probabilities. So,

P(cxd)=cd2(x+1)2 dx=2cd(x+1)2 dx

Use the formula xndx=xn+1n+1 and integrate.

2cd(x+1)2 dx=2((x+1)2+12+1)cd=2(1x+1)cd

(a)

To calculate P(0<x<12), use the Fundamental theorem abf(x) dx=F(b)F(a) and apply the limits on 2(1x+1)cd.

2(1x+1)012=2[(112+1)(10+1)]=2=2(233)=2(13)

Multiply.

2(13)=23

Thus, the probability of P(0<x<12) is 23.

(b)

To calculate P(14<x<34), use the Fundamental theorem abf(x) dx=F(b)F(a) and apply the limits on 2(1x+1)cd

### 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

Find more solutions based on key concepts
In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the numerical value of each expression. 5. (a) sech 0 (b) cosh11

Single Variable Calculus: Early Transcendentals, Volume I

A population of N = 7 scores has a mean of = 13. What is the value of X for this population?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 5762, sketch the straight line defined by the given linear equation by finding the x- and y-interc...

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

Solve the equation in problem 1-6.; 5.

Mathematical Applications for the Management, Life, and Social Sciences

Solve the inequality. 49. |x 4| 1

Single Variable Calculus: Early Transcendentals

Simplify: 2436

Elementary Technical Mathematics

limx5x225x29x+20= a) 1 b) 10 c) d) does not exist

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

True or False:

Study Guide for Stewart's Multivariable Calculus, 8th 