The Laplace distribution (also called the double exponential distribution) with parameters θ and λ has a pdf with kernel e-λ|x-θ| . This resembles the pdfs for the normal and exponential distributions. Compared to the normal distribution, the Laplace distribution uses an absolute value in place of a square. This will cause the Laplace distribution to have heavier tails than a normal distribution. The Laplace distribution can also be viewed as a shifted and mirrored version of an exponential distribution: It is symmetric about θ and each half looks like an exponential distribution with parameter λ.

a) Compute the mean and variance of a Laplace random variable.

b) Write an R function dlaplace() to compute the pdf of a Laplace random variable.

c) Write an R function plaplace() to compute the cdf of a Laplace random variable.

d) Use your functions to determine the following: