Find the p.d.f of y from p.d.f of x

[wldnrp13579]

Homework Statement

f_x(X) ={ 1/4 0 < x < 1,
{ 3/8 3 < x < 5,
{ 0 otherwise

Let Y = 1/X. Find the probability density function f_y (y) for Y .

Homework Equations

The Attempt at a Solution

Fy(x)=P(Y<x)=P(1/X<x)=P(X>1/x)..

i can't go over more than this

 

[haruspex]

What's the relationship between P(X<x) and P(X>x) for a continuous distribution.

 

[Ray Vickson]

Homework Statement

f_x(X) ={ 1/4 0 < x < 1,
{ 3/8 3 < x < 5,
{ 0 otherwise

Let Y = 1/X. Find the probability density function f_y (y) for Y .

Homework Equations

The Attempt at a Solution

Fy(x)=P(Y<x)=P(1/X<x)=P(X>1/x)..

i can't go over more than this

You have the probability density of X. What is stopping you from computing G(t) =P(X > t)?