# Calculating covariance

1. Jun 22, 2010

### logarithmic

1. The problem statement, all variables and given/known data
Find the Cov(X(t), X(t+s)) where X(t) = N(t+1)-N(t), where N(t) is a poisson process with parameter $$\lambda$$.

2. Relevant equations

3. The attempt at a solution
X(t) should be poisson distributed with mean $$1\lambda$$ by stationary increments, and X(t+s) should be poisson distributed with mean $$\lambda$$. This reduces to finding the covariance of 2 dependent poisson($$\lambda$$) random variables (since X(t) and X(t+s) is dependent, so the answer isn't just = variance = $$\lambda$$). Now what do I do?