- #1
andrew21nz
- 2
- 0
Hey
I'm really struggling with this:
What is the expected value of a poisson process (rate λ, time t) given that at least one even has occured? I was told the best way was to find the conditional distribution first.
So this is: P(Xt=z | Xt≥1)
= P(Xt=z, Xt≥1) / (PXt≥1)
= P(Xt=z) / (PXt≥1) for z=1, 2...
= (e-λt * (λt)z/z!)
-----------------
... 1 - e-λt
That's what I keep coming back to. I think it should come out as something poisson? That way the expected value is just the parameter. Clearly I'm doing something wrong and it's really frustrating me
Sorry if it's messy, I couldn't get the Latex thing working
Thanks in advance for your help :)
I'm really struggling with this:
What is the expected value of a poisson process (rate λ, time t) given that at least one even has occured? I was told the best way was to find the conditional distribution first.
So this is: P(Xt=z | Xt≥1)
= P(Xt=z, Xt≥1) / (PXt≥1)
= P(Xt=z) / (PXt≥1) for z=1, 2...
= (e-λt * (λt)z/z!)
-----------------
... 1 - e-λt
That's what I keep coming back to. I think it should come out as something poisson? That way the expected value is just the parameter. Clearly I'm doing something wrong and it's really frustrating me
Sorry if it's messy, I couldn't get the Latex thing working
Thanks in advance for your help :)