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I am given Poisson process $X_t$ which has intensity $\lambda$. Is there a way to count the mean for it? I am terribly confused. I am able to count the mean of a variable which has a Poisson distribution (and that is $\lambda$), but as I understand it is not the same.

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$X_t\sim \text{po}(\lambda t)$ and hence $E[X_t]=\lambda t$. – Stefan Hansen May 22 '12 at 10:50
You should post this as an answer :) – Andrius Naruševičius May 22 '12 at 11:02
Makes one wonder what kind of an introduction to Poisson processes you were exposed to, which does not comprise this. – Did May 22 '12 at 13:42
Want a honest answer? I did not study. For several reasons, only one of them being I hate what I study :( I have this one last exam. After that (assuming I did not fail it), I would continue my job as a programmer which I enjoy. I just need to remove the stage of studies from my life and thus I needed help. Thanks :) – Andrius Naruševičius May 22 '12 at 18:37
up vote 1 down vote accepted

A main property of a Poisson proces with parameter $\lambda$ is that $X_t\sim \text{po}(\lambda t)$ for every $t>0$. Especially we have $E[X_t]=λt$ for $t>0$.

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Appreciated :)) – Andrius Naruševičius May 22 '12 at 12:00

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