Arrivals of passengers at a bus stop form a Poisson process ${N(t), t ≥ 0}$ with rate $\lambda = 2$ per unit of time. Assume that a bus departed at time $t = 0$ leaving no customers behind. Let $T$ be the arrival time of the next bus. Then, the number of passengers present when it arrives is $N(T)$. Suppose that the bus arrival time $T$ is independent of the Poisson process and that $T ∼ U[0,1]$. By first conditioning on $T$, determine the mean and the variance of the number of passengers present when the next bus arrives.
I'm kind of confused on how to start this. I can't quite figure out if this would be a conditional probability where we apply Bayes Theorem to $E[N(t)|t=T]$ or if this is actually a compound Poisson process. If it is a compound Poisson process I'm not quite sure how to set that up.