Jane Street–styleTraderAssistant TraderQuestion #242
What is the expected value of the product when rolling a six-sided die and an eight-sided die?
Free worked solution · Quant Blueprint
63/4 = 15.75, assuming independent fair dice numbered from one.
- The six-sided die has mean (1+6)/2 = 7/2; the eight-sided die has mean (1+8)/2 = 9/2.
- Independence permits E(XY) = E(X)E(Y).
- Multiply: (7/2)(9/2) = 63/4. Alternatively average all 48 products; the double sum factors into (Σx)(Σy)/48.
Common mistake
Multiplying means requires independence or zero covariance. It is not a general identity for two random variables.
Follow-up
In general E(XY) = E(X)E(Y) + Cov(X,Y). Ask about dependence before using the shortcut.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
More Jane Street–Style Trader Questions
A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the center cube?You flip 4 fair coins and receive $1 for each coin that lands heads. What is the expected value of your total winnings?If you roll two dice, and you have the option to roll again and get paid the highest roll, when is it optimal to reroll?What is 2,000,000 minus 2,022?How many digits does 99 raised to the 99th power have?
Practice the Reasoning Behind the Answer
Bring your target roles and interview timeline to a free quant consult. Discuss your preparation priorities and how Quant Blueprint’s lessons, practice and mock interviews can help.
Book a Free Quant ConsultYour goals · your preparation · your next steps