Question

Let X be a random variable with PDF fX. Find the PDF of the random variable Y=eX for each of the following cases:

For general fX, when y>0, fY(y)=


- unanswered fX(eyy) fX(ln yy) fX(ln y)y none of the above
When fX(x) = {1/3,0,if −2<x≤1,otherwise,

we have fY(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 fX(x) = {2e−2x,0,if x>0,otherwise,

we have fY(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= - unanswered

Answer 1

For general fX, when y>0, fY(y)=

Solution: f_x(ln(y))/y





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

we have fY(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.)


Solution: g(y) = 1/(3*y)

a = e^(-2)

b = e




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

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

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


Solution: g(y) = 2/(y^(3))

a= 1





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


Solution: 1/sqrt(2pi) * (e^(-ln(x))^2/2)/y