# Homework Help - Markov Chains

1. Sep 20, 2009

### spacecataz

1. The problem statement, all variables and given/known data

Suppose X is a Poisson random variable with mean 5. Suppose Zn = nX + 3 for n = 0, 1, 2, . . . . (a) Does Z0 , Z1 , . . . have the Markov property? (b) If Z0 , Z1 , . . . has the Markov property, is it time-homogeneous?

Suppose X and Y are independent Poisson random variable both having mean 5. Suppose Zn = nX + Y for n = 0, 1, 2, . . . . (a) Does Z0 , Z1 , . . . have the Markov property? (b) If Z0 , Z1 , . . . has the Markov property, is it time-homogeneous?

2. Relevant equations

pmf of Poisson distribution: ($$\lambda^{k}*e^{-\lambda}$$)/k!

3. The attempt at a solution
I'm not really sure where to start with this. I'm inclined to say that for the first part it is a Markov chain but I'm not sure if I need to use the pmf of the Poisson distribution.

I'm also inclined to say that the second part is not a Markov chain because of Y, but I'm really not sure.

Any resources or guidance with this would be greatly appreciated.

Thanks!