Expected Value and markov conditional distribution

Let X be a non-negative, continuous random variable with mgf given by;
mx(t)=E(e^tx)=(1/(1-2t))e^(1/(1-2t))

Also let y be a random variable such that Y given X=x has a poisson distribution with parameter 2x so that Pr(Y=y given X=x) = (2x^y.e^-2x)/y!

Find E(Y) . it is given E(X)=3

Also


Let {Nt}t>/0be a Markov chain such that N0 = 0 and
P(m,n)= (e^(m-n-1/e))/(n-m)!

Find the conditional distribution of (Nt+1-Nt) given Nt=m

If anyone could tell me how to go about either of these questions it would be greatly appreciated.

I also know the value of E(Y|X)= 2x as Pr(Y|X) is modelled by a poisson distribution, im just not sure how to transform this into my E(Y). Can it be done by E(Y|X)E(X)?

You can use law of iteration to find E(Y)

E[E(Y|X)] = E(2X)
E(Y) = 2E(X)
E(Y) = 2*3
E(Y) = 6

Thanks Jesswyn i worked that out eventually, and now feel really stupid lol, can anyone give me an idea of how to start the markov chain problem?

hahah guess what...im figuring it also.... i think we are doing the same assignment....hahaha