Well the best way is to see that if X follows a Laplace distribution, so does -X, since the pdf is symmetric over 0... Then for x>0,
given the laplace distribution. f(x)=0.5*e^(-|x|)
How do you integrate in order to find the cdf for x>0 (I have no problem finding the solution for x<0)
The solution is 1-0.5*e^(-x)
I would be very grateful for a detailed solution or a link to a website were I could find it.
Thanks in advance!
Thanks a lot for your help, your answer is very clear,
another thing: (I don't know whether I should start a new thread for this, I changed the title of the original post to make it clear that there is a 2nd part to the original question)
how do I derive the kurtosis of the laplace function using an integral of the pdf? I will have to integrate by parts, but how?
Here, the "location" is and the "scale" is . But we know that the variance is , hence
So the kurtosis will be (symmetry over 0).
You can do 3 (I think) successive integrations by parts or you can simply recognize the gamma function, which is much easier :P