Question

Part A

The variable X(random variable) has a density function of the following

f(x) = {5e^-5x if 0<= x < infinity and 0 otherwise}

Calculate E(e^x)

Part B

Let X be a continuous random variable with probability density function

f (x) = {6/x² if 2<x<3 and 0 otherwise }

Find E (ln (X)).
.

Answer 1

Part A

for

Part B

for 2 < x < 3

Let t = ln(x) then range of t is ln(2) to ln(3)

dt = dx/x

and x = e^t