
Find the distribution
Hi
Problem:
Let be a Poisson process with rate .
For define
Compute the distribution and the expected value of for .
I have calculated the probability of being odd or even, which will control probability of being 1 or +1.
Fix t > 0
Similarily for probability of being even.
How do I go about finding the distribution function, I assume I have found something like density function?
Thx

Hello,
Isn't there something like a Bernoulli distribution ? :P

How would I go about finding the distribution function from this. I looked at the bernoulli distribution, I didnīt really see how I could use it for my particular problem though. Help on this area would be appreciated.
Also, my attempt on the expected value gave me .
Could this be correct? It seems reasonable that the expected value tends to zero as , but also that the expected value is not zero when t is small, because it is more likely that is even for small t.

I don't understand your problem actually.
Y(t) can only take two values : 1 and 1.
Let
We have and
And this is exactly a Bernoulli distribution over {1,1} with parameter p(t)
Why do you absolutely want a distribution function ? You can write it if you really want to, but it's not really necessary...

Hi
You understand it correctly, and yes it should be a bernoulli distribution.
Can one say that has independant and stationary increments?