Problem 6 (5pt) Compute the mean, variance and kurtosis of the probability distribution with density on the real axis (2) f(x) = e Recall that the mean , variance V and kurtosis k are expressed in terms of moments of the random variable X as (3) A = EX , V = E(X -/)'], E[(X -1) 4 ] K = V2 A normal (Gaussian) distribution has kurtosis Ky = 3. In order to compare with a Gaussian, it is customary to define the excess kurtosis as Kexcess = K-3