Citadel–styleTraderQuantitative TraderQuestion #128
What is the expected value of the cube of a fair six-sided die roll?
Free worked solution · Quant Blueprint
E(X³) = 147/2 = 73.5.
- Each value from one to six has probability 1/6. Apply the payoff function before averaging.
- The cubes sum to 1 + 8 + 27 + 64 + 125 + 216 = 441.
- Divide by six: 441/6 = 73.5. The identity Σk³ = [n(n+1)/2]² gives the same sum.
Common mistake
E(X³) is not [E(X)]³: cubing is nonlinear. The latter would give 42.875.
Follow-up
For a fair n-sided die numbered 1 through n, E(X³) = n(n+1)²/4.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
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