Question

A continuous random variable is said to have a Laplace(?, b) distribution if its probability density function is given by f_X(x) = ?/2b exp (-?x - ?? / b), where ? is a real number and b>0. (i). If X ~ Laplace(0,1), find E(X) and Var(X). (ii). If X ~ Laplace(0,1) and Y = bX + ?, show Y ~ Laplace(?, b). (iii). If W ~ Laplace(2,8), find E(W) and Var(W).

          A continuous random variable is said to have a Laplace(?, b) distribution if its probability density function is given by
f_X(x) = ?/2b exp (-?x - ?? / b),
where ? is a real number and b>0.
(i). If X ~ Laplace(0,1), find E(X) and Var(X).
(ii). If X ~ Laplace(0,1) and Y = bX + ?, show Y ~ Laplace(?, b).
(iii). If W ~ Laplace(2,8), find E(W) and Var(W).

A continuous random variable is said to have a Laplace(?, b) distribution if its probability density function is given by
fX(x) = ?/2b exp (-?x - ?? / b),
where ? is a real number and b>0.
(i). If X Laplace(0,1), find E(X) and Var(X).
(ii). If X Laplace(0,1) and Y = bX + ?, show Y Laplace(?, b).
(iii). If W Laplace(2,8), find E(W) and Var(W).

Added by Matthew R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

05/11/2024

Step 1

Step 1: Understanding the Laplace Distribution The Laplace distribution, denoted as Laplace(u, b), is defined by its probability density function (PDF): \[ f(x) = \frac{1}{2b} \exp\left(-\frac{|x-u|}{b}\right) \] where \(u\) is the location parameter and \(b > 0\) Show more…

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A continuous random variable is said to have a Laplace(μ, b) distribution if its probability density function is given by f_X(x) = 1/(2b) exp(-|x-μ|/b), where μ is a real number and b > 0. (i). If X ~ Laplace(0,1), find E(X) and Var(X). (ii). If X ~ Laplace(0,1) and Y = bX + μ, show Y ~ Laplace(μ, b). (iii). If W ~ Laplace(2,8), find E(W) and Var(W).