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 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 x1

f(x)=dx

=*

=

=+

=1

Thus the graph of cdf of x becomes,