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!

Quote:

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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?

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

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

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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.