here is a probability model Problem. Please try to answer this question and explain your answer. Thank you~!

4. Vehicles arrive at Joe's Bar and Grill according to a Poisson process, N(t), with intensity o, The number of individuals in the j'th arriving vehicle is a random variable, Y,, such that P(Yj = k) = Pk, k = 1,2, ...,6. The Y,'s are i.i.d. All individuals in the j'th arriving vehicle enter and leave together and stay in the restaurant a random amount of time, Z,, where the Zj's are i.i.d. exp() = 1/30), thus E(Z;) = 30. Time is measured in minutes. Assume that {N(t) }co, (Y,}fe, and {Z}}f, are independent. Define X(t) = the number of individuals that have arrived in (0, t]. and Y (t) = the number of individuals that are in Joe's B&G at time t. Assume that Y (0) = 0. Evaluate, in terms of 6, {px}=1 and t, ( a) x(t) (2), (b) P(X(t) = 0), ( c) by (t) ( 2 ) (d) E(Y (t) ) and lim E(Y(t) )