Thread: Probability Distribution Function Help

Given the probability distribution function:




Determine the:

1. Probability density function.
2. The mean.
3. The median.

Hello,
I am really struggling with this subject area, this is an example I have found, would someone be able to go through a solution so I can begin to understand it a bit more.
Appreciate any help in advance.
Thanks.

Originally Posted by jscfc

Given the probability distribution function:




Determine the:

1. Probability density function.
2. The mean.
3. The median.

Hello,
I am really struggling with this subject area, this is an example I have found, would someone be able to go through a solution so I can begin to understand it a bit more.
Appreciate any help in advance.
Thanks.

First you have a typo in your problem.
Second we are not mind readers so please tell us that the function is the Cumulative distribution function
Cumulative distribution function - Wikipedia, the free encyclopedia

Your book or the above wiki will tell you that the CDF is the integral of the PDF



So to undo an integral we will use the fundamental theorem of calculus to take the derivative of

This will give the PDF

This will answer the rest of you question.

Exponential distribution - Wikipedia, the free encyclopedia

If you get stuck please post some work so we can see where.