Question

The PDF of exp(X)

Let X be a random variable with PDF f_X. Find the PDF of the random variable Y=e^X for each of the following cases:

For general f_X, when y>0, f_Y(y)=

f_X(ln y)
---------
y


When f_X(x) = {1/3,0,if −2<x≤1,otherwise,

we have f_Y(y) = {g(y),0,if a<y≤b,otherwise.

Give a formula for g(y) and the values of a and b using standard notation . (In your answers, you may use the symbol 'e' to denote the base of the natural logarithm.)

g(y)= unanswered



a= unanswered




b= unanswered




When f_X(x) = {2e−2x,0,if x>0,otherwise,

we have f_Y(y) = {g(y),0,if a<y,otherwise.

Give a formula for g(y) and the value of a using the standard notation .

g(y)= unanswered



a= 1


When X is a standard normal random variable, we have, for y>0, f_Y(y)=

(2*π)^-1/2 * e^-((ln y)^2)/2)
----------------
y

PLEASE, COULD YOU PROVIDE THE OTHER ANSWERS TO THIS PROBLEM???

Answer 1

g(y)=1/(3y)
a=e^(-2)
b=e^1