# Thread: Expected Value and markov conditional distribution

1. ## 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>/0
be 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.

2. 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)?

3. 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

4. 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?

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