IMC Trading–styleTraderTrading InternQuestion #57
What is the variance of a six-sided dice roll?
Free worked solution · Quant Blueprint
35/12, approximately 2.9167, assuming a fair die numbered one to six.
- The mean is (1+2+3+4+5+6)/6 = 7/2.
- The second moment is (1+4+9+16+25+36)/6 = 91/6.
- Use Var(X) = E(X²) − E(X)² = 91/6 − 49/4 = 35/12.
Common mistake
Variance is the mean squared deviation, not the mean absolute deviation or standard deviation.
Follow-up
For a fair die numbered one through n, Var(X) = (n² − 1)/12. For two independent six-sided dice, the variance of the sum is 35/6.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
More IMC Trading–Style Trader Questions
You have a 100-story building and two balls that break when dropped from too high a floor. What is the minimum number of drops needed on average to determine the highest floor from which a ball can be safely dropped?Given 20 horses and 5 tracks, what is the minimum number of races required to determine the three fastest horses, assuming you can race up to 5 horses at a time and there is no timing, only order of finish in each race?What is the probability of rolling an increasing sequence when you roll a die three times?You have a 4x4 grid and three balls. If you manage to get at least 2 balls in the same row or column, you win. What is the probability of winning?How much would the average global sea level rise if the mass of Mount Everest was submerged into the ocean?
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