2. Stochastic Processes

Poisson Processes — Quiz

Test your understanding of poisson processes with 5 practice questions.

Practice Questions

Question 1

In a homogeneous Poisson process with rate $\lambda$, conditional on $N(t)=n$, the joint distribution of the $n$ event times within $[0,t]$ is equivalent to:

Question 2

The memoryless property of exponential interarrival times in a Poisson process implies that $P(T>s+t\mid T>s)$ equals:

Question 3

In simulating a Poisson process, the time $S_k$ of the $k$th event is given by $S_k=\sum_{i=1}^kX_i$ where $X_i\sim\mathrm{Exp}(\lambda)$. The distribution of $S_k$ is:

Question 4

For a homogeneous Poisson process with rate $\lambda$, the probability of observing at least one event in an interval of length $t$ is:

Question 5

In a compound Poisson process $S(t)=\sum_{i=1}^{N(t)}J_i$ with $N(t)$ a Poisson process of rate $\lambda$ and jump sizes $J_i$, the expected value $E[S(t)]$ is: