# Independent Random Variables

• Nov 29th 2010, 11:24 PM
DEUCSB
Independent Random Variables
"Let X and Y be two independent random variables with the same probability density function given by

f(x)= (
e^(-x) if 0<x<inf.
0 elsewhere
)

Show that g, the probability density function of X/Y, is given by

g(t)=(
1/(1+t)^2 if 0<t<inf.
0 t<=inf.
"

Thanks!
• Nov 30th 2010, 12:11 AM
mr fantastic
Quote:

Originally Posted by DEUCSB
"Let X and Y be two independent random variables with the same probability density function given by

f(x)= (
e^(-x) if 0<x<inf.
0 elsewhere
)

Show that g, the probability density function of X/Y, is given by

g(t)=(
1/(1+t)^2 if 0<t<inf.
0 t<=inf.
"

Thanks!

What have you tried? Where are you stuck?
• Nov 30th 2010, 01:04 AM
DEUCSB
I have found the density functions for both of x and y but dont know how to convert that to X/Y
• Dec 1st 2010, 03:52 AM
mr fantastic
Quote:

Originally Posted by DEUCSB
I have found the density functions for both of x and y but dont know how to convert that to X/Y

You were told the density functions. Have you done any research eg. Google the key words

ratio distribution

quotient random variables

etc.

What have you been taught in class regarding the algebra of random variables? eg. Change of variable theorem.