4. Evolution

Speciation — Quiz

Test your understanding of speciation with 5 practice questions.

Practice Questions

Question 1

Which of the following best describes the Markov property for a stochastic process $\{X_t\}$?

Question 2

Consider a discrete-time Markov chain with transition matrix $P=\begin{pmatrix}0.6 & 0.4 \\ 0.3 & 0.7\end{pmatrix}$ and initial distribution $\pi_0=(1,0)$. What is the distribution $\pi_1$ after one step?

Question 3

For the Markov chain in Question 2, what is the stationary distribution $\pi=(\pi_1,\pi_2)$ satisfying $\pi P=\pi$?

Question 4

In a continuous-time Markov process with generator $Q=(q_{ij})$, which condition must hold for each row $i$?

Question 5

In a credit risk model, a firm's rating follows a two-state discrete-time Markov chain with transition matrix $P=\begin{pmatrix}0.85 & 0.15 \\ 0 & 1\end{pmatrix}$ where state 1 is default. If the firm is initially healthy (state 0), what is the probability it defaults within two periods?