6. Let X be a random variable having pdf :{ (a) (b) (d) fx(x) = A exp{-X(x-μ)} 0 Show that fx(x) is a legitimate pdf. Find the cdf of X. if x > μ, otherwise. Using the definition of E[X], find the mean of X. Find the mgf Mx (t) of X, and use it to find u.

TF.8

x > 1 A RV X has the PDF fx(x) = otherwise (a) Find the MGF Mx(t) of X and clearly define the values of t for which it exists. (b) Find the mean (µ) and variance (o?) of the RV X using the MGF from (a).

1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise