A continuous random variable is said to have a Laplace(, b) distribution [ 14 ] if its

A continuous random variable is said to have a Laplace(μ, b) distribution [14] if its PDF is given by

where μ ∈ R and b > 0.

a. If X ∼ Laplace(0, 1), find EX and Var(X).

b. If X ∼ Laplace(0, 1) and Y = bX + μ, show that Y ∼ Laplace(μ, b).

c. Let Y ∼ Laplace(μ, b), where μ ∈ R and b > 0. Find EY and V ar(Y).

Transcribed Image Text:

fx(x) = 26 2b 1 26 -exp exp(") exp(-) |x-μ|| b if x < μ if χ Σμ