Let fyt Y Y 3e X Compute the probability density function o

Let fy(t) = Y: Y= 3e X. Compute the probability density function of Y be the random variable defined by lambda = 10, and let X be an exponential random variable with parameter

Solution

given

f(x) =10 e^-10x                   x>0

Y= 3e^X

X = log Y/3

dx/dy =1/y

then

f(y) =f(x(y))dx/dy

    =10e^-10log(y/3) 1/y

=10 (y/3)^-10 1/y

=10*3¹⁰ y^-11            Y>3