DRW Interview Questions (2026-2027)

I just finished DRW's Quantitative Researcher online test (OT), and it was extremely difficult, covering multiple areas including linear algebra, probability theory, stochastic processes, and calculus. I've compiled the questions to share with everyone, hoping they will be helpful. --- Below are 7 questions, set to 188 points for visibility; the questions are very challenging. The following content requires points higher than 188. You can already browse 1. (Question 1 of 7) You're given a coin that you know lands on one side with probability 2/3, but there's a 50/50 chance that the side it's biased towards is heads or tails. Suppose you flip the coin 7 times and get 5 heads. What is the probability that the coin is biased towards heads? Express your answer to 2 decimal places. 2. (Question 2 of 7) Define $f(x, y, z)$ as the sum of the eigenvalues of $M^{-1}$, where $M$ is defined as $$M(x, y, z) = \begin{pmatrix} x & 0 & y \ 0 & x & y \ y & y & z \end{pmatrix}$$ Compute $$\frac{\partial^2}{\partial y \partial x} f(x, y, 0)|{(x,y)=(8,-4)} - \frac{\partial}{\partial x} f(x, y, 0)|{(x,y)=(8,-4)}$$ Express your answer to 3 decimal places. 3. (Question 3 of 7) Suppose passengers arrive at a bus station according to a Poisson process with rate 18, i.e., the number of passengers $k$ who arrive in an interval of time $\Delta t$ is distributed as $\frac{e^{-18\Delta t}(18\Delta t)^k}{k!}$ where $k \in \mathbb{Z}$ and $k \ge 0$. Additionally, the arrival time of the bus follows an exponential distribution with parameter 6, i.e., the probability density of the time $\tau$ between one arrival and the next is $6e^{-6\tau}$. Calculate the expected number of passengers on any given bus. Express your answer to 1 decimal place. 4. (Question 4 of 7) You have 3 identical-looking mystery boxes. You know that one box contains figurine A, one contains figurine B, and one contains figurine C. However, you do not know which box contains which figurine. Unopened boxes can be sold for $3 each. Once a box is opened, you can only sell it for the market price of the figurine inside. The figurine prices are: Figurine A: $1, Figurine B: $3, Figurine C: $5. Your goal is to open some, none, or all of the mystery boxes in a way that maximizes your expected profit (i.e. the total amount of money you receive from selling all mystery boxes, opened or not). Under the optimal box-opening strategy (maximizing the expected profit), what is the value of the expected profit over standard deviation of your profit, i.e., $\frac{E(P)}{\sqrt{Var(P)}}$ where $P$ is your profit. Express your answer to 2 decimal places. 5. (Question 5 of 7) On a distant planet, there are two political parties A and B. Every 4 years, there is an election in which citizens choose a party and vote A or B. Every citizen votes in every election. The population remains constant. Immediately after every election, each voter may switch parties. The A voters switch with probability 15%, while the B voters switch with probability 14%, due to a slight media bias against the B party. In a certain election, the B party wins 70%-30%. In the election 10,000 years later, what is the expected vote for the B party? Express your answer as a percentage, to 2 decimal places. 6. (Question 6 of 7) You are given a 3 x 3 correlation matrix $\Sigma$: $$\Sigma = \begin{pmatrix} 1 & 1/2 & 1/4 \ 1/2 & 1 & x \ 1/4 & x & 1 \end{pmatrix}$$ What is the difference between the maximum and minimum possible values of $x$, i.e. $x_{max} - x_{min}$? Express your answer to 3 decimal places. 7. (Question 7 of 7) In the 2 x 2 matrix $M$, each element is a random variable: $$M = \begin{pmatrix} x & y \ z & w \end{pmatrix}$$ where $x \sim N(2, 2)$, $y \sim N(3, 1)$, $z \sim U(1, 2) $, $w \sim U(3, 4)$. $N(\mu, \sigma)$ denotes the normal distribution with mean $\mu$ and standard deviation $\sigma$ (note the atypical notation), and $U(a,b)$ denotes the uniform distribution in $[a, b]$. In addition, the random variables $x$ and $w$ are correlated, with a correlation coefficient $\rho = 2/3$. All others are uncorrelated. What is the fair price for a contract which pays out the determinant of $M$? Express your answer to 2 decimal places. --- I've almost remembered the question; I hope it helps everyone. Requesting points! Requesting points! Requesting points! Wishing everyone gets an offer soon and a successful job application!