The Laplace distribution, also known as a double exponential, has a pdf given by:
Find the theoretical mean and variance of a laplace distribution. (Hint: Integrals of absolute values should be done as a positive and negative part, in this case, with limits from -∞ to μ and from μ to ∞.)
I am not sure how to even go about this problem. I think you would have to set it as an integral using the following formula for the expected value of the mean: (lambda would be a constant)
If this is correct how would you solve this integral?