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# Sketch the graphs of the following pdfs and find and ISBN: 9780321923271 41

## Solution for problem 12E Chapter 3.1

Probability and Statistical Inference | 9th Edition

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Problem 12E

Sketch the graphs of the following pdfs and find and sketch the graphs of the cdfs associated with these distributions (note carefully the relationship between the shape of the graph of the pdf and the concavity of the graph of the cdf): Step-by-Step Solution:

Step 1 of 4:

Here for the given probability density function we have to find the respective cumulative density function and then we have to sketch their graphs.

Step 2 of 4:

(a)

The probability density function given here is

f(x)= ;-1<x<1

To sketch the graph of the given pdf we have to find the value of f(x) in the given range -1<x<1.

At x=-1

f(x)= =1.5

At x=0

f(x)= *0

=0

At x=1

f(x)= *1

= The graph of the pdf is Now we will find the cumulative density function of f(x).The cdf(cumulative density function) of x is denoted by F(x)

It is given by

F(x)= dx

If x -1, then F(x)=0.

If -1<x<1, then F(x) becomes

F(x)= f(x)dx

=   dx

=  = ( -( = + = At x=-1

F(x)= =0

At x=0

F(x)= = At x=1

F(x)= =1

At x 1

f(x)=   dx

= * = = + =1

Thus the graph of cdf of x becomes, Step 3 of 4

Step 4 of 4

##### ISBN: 9780321923271

This full solution covers the following key subjects: Graphs, sketch, graph, associated, concavity. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The full step-by-step solution to problem: 12E from chapter: 3.1 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Since the solution to 12E from 3.1 chapter was answered, more than 451 students have viewed the full step-by-step answer. The answer to “Sketch the graphs of the following pdfs and find and sketch the graphs of the cdfs associated with these distributions (note carefully the relationship between the shape of the graph of the pdf and the concavity of the graph of the cdf):” is broken down into a number of easy to follow steps, and 42 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9.

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