MHB Finding the PMF of Y with Known X

[Dustinsfl]

How do I find the PMF of Y when I know X?
\[
Y = \sin\Big(\frac{\pi}{2X}\Big)
\]
and
\[
p_X[k] = \frac{1}{5}
\]
for \(k = 0,1,\ldots, 4\).

 

[Siron]

Maybe there're several ways to solve this problem. It's clear that $Y$ is a transformation of $X$. So have you seen any theorems about characteristic funtions of transformated random variables?

EDIT:
I now see that this problem is already solved.

 

[MarkFL]

...EDIT:
I now see that this problem is already solved.

Well, the [SOLVED] prefix has been added, but I see no solution...

 

[chisigma]

How do I find the PMF of Y when I know X?
\[
Y = \sin\Big(\frac{\pi}{2X}\Big)
\]
and
\[
p_X[k] = \frac{1}{5}
\]
for \(k = 0,1,\ldots, 4\).

There is a point not clear: writing $\displaystyle p_X[k] = \frac{1}{5}, k= 0,1,2,3,4$ means writing $\displaystyle P\{X=k \} = \frac{1}{5}, k= 0,1,2,3,4$?...

Kind regards

$\chi$ $\sigma$

 

[chisigma]

There is a point not clear: writing $\displaystyle p_X[k] = \frac{1}{5}, k= 0,1,2,3,4$ means writing $\displaystyle P\{X=k \} = \frac{1}{5}, k= 0,1,2,3,4$?...

Kind regards

$\chi$ $\sigma$

The reason of my question is that for X=0 defining $\displaystyle Y = \sin \frac{\pi}{2\ X}$ is a little difficult task (Dull)...

Kind regards

$\chi$ $\sigma$