# Given probability density function find its cumulative distribution function

#### sofanglom

##### New member
Hi Here's my problem along with what I've done.

Here is the problem:

That is the p.d.f. of a random variable X.

I have to find the cdf.

I don't know which I should do so I tried it two ways. First:

$\int_{-1}^{1} \ \frac{2}{\pi(1+x^{2})} dx = {{\frac{2}{\pi} arctan(x)]}^{1}}_{-1}=1$

Second:

$\int_{-1}^{x} \ \frac{2}{\pi(1+t^{2})} dt = {{\frac{2}{\pi} arctan(x)]}^{x}}_{-1}=\frac{2(arctan(x)+\frac{\pi}{4}}{\pi}$

Which one is the required CDF for X?

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
Hi, and welcome to the forum!

Which one is the required CDF for X?
The second one, except for the missing closing parenthesis. That is, the CDF is $\dfrac{2}{\pi}\arctan x+\dfrac12$.