find the density function of z=tan(Y)

?

i had a similar question

X~U(0,1)

find the density function of W=a+bx

the solution is

W~U(a,a+b)

how to solve the first question ??

Printable View

- Feb 2nd 2010, 02:57 AMtransgalacticdensity function question..

find the density function of z=tan(Y)

?

i had a similar question

X~U(0,1)

find the density function of W=a+bx

the solution is

W~U(a,a+b)

how to solve the first question ?? - Feb 2nd 2010, 05:32 PMmatheagle
READ below, I think the orginal density is WRONG.

USE which is easy to derive.

It's the derivatives of the CDFs, it's just calc 1.

So, on

and giving you

Hence

I THINK there is a problem here, we should be getting a Cauchy.

I think the original density should be a uniform on because tangent isn't defined at - Feb 2nd 2010, 05:42 PMmatheagle
The second one is obvious.

on 0<x<1.

If you let W=a+bX then W exists on (a,a+b), by letting X=0 and X=1.

Next, I will show that W is uniform on that interval.

USE

With w=a+bx we have

So, USE IF b>0.

which is a uniform density.