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)?
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.