# Question: For a Laplace random variable Whose PDF is given by Find

For a Laplace random variable Whose PDF is given by

Find the following:

(a) The characteristic function, ϕ X (ω),

(b) The Taylor series expansion of ϕX (ω),

(c) A general expression for the k th moment of X.

Find the following:

(a) The characteristic function, ϕ X (ω),

(b) The Taylor series expansion of ϕX (ω),

(c) A general expression for the k th moment of X.

**View Solution:**## Answer to relevant Questions

An Erlang Random variable has a PDF of the form (a) Find the characteristic function, ϕX( ω) . (b) Find the Taylor series expansion of ϕX( ω) . (c) Find a general expression for the k th moment of X. Derive a formula expressing the variance of a random variable in terms of its factorial moments. Derive an expression for the moment- generating function of a Rayleigh random variable whose PDF is Prove that for a random variable X with mean µX , Where n is any positive integer. A nonnegative random variable X has moments which are known to be E [X] = 1 , E [X2] = 2 , E [X3] = 5 , E [X4] = 9 , E [X5] = 14 , E [X6] = 33. (a) Show that for any nonnegative random variable, (a) Show that for any ...Post your question