The Laplace distribution has PDF fx1 2ex for all real x The

The Laplace distribution has PDF
f(x)=1/ 2^e|x|
for all real x. The Laplace distribution is also called a symmetrized Exponential distribution. Explain this in the following two ways.
(a) Plot the PDFs and explain how they relate. (b) Let X Expo(1) and S be a random sign (1 or 1, with equal probabilities), with S and X independent. Find the PDF of SX (by rst nding the CDF), and compare the PDF of SX and the Laplace PDF.

Solution