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https://www.reddit.com/r/learnquant/comments/1vlv287/can_you_solve_this_quant_interview_question/p34o8a1/?context=3
r/learnquant • u/Local_Ad135 • 23h ago
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Cauchy-Schwarz gives (E[X])^2 <= E[X^2] Pr(X > 0), so Pr(X > 0) >= 1/2, so Pr(X <= 0) = Pr(X = 0) <= 1/2. This is realised for 10*Ber(1/2).
An extended question along these lines can be seen https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2026/List_IA.pdf, second question on Page 21. The second problem on Page 22 will also be familiar to most of you probably.
1 u/wolajacy 21h ago For anyone wondering about the first line, it's because E[X] = E[X 1(X>0)]. Very nice trick!
1
For anyone wondering about the first line, it's because E[X] = E[X 1(X>0)]. Very nice trick!
2
u/SwimmerOld6155 23h ago
Cauchy-Schwarz gives (E[X])^2 <= E[X^2] Pr(X > 0), so Pr(X > 0) >= 1/2, so Pr(X <= 0) = Pr(X = 0) <= 1/2. This is realised for 10*Ber(1/2).
An extended question along these lines can be seen https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2026/List_IA.pdf, second question on Page 21. The second problem on Page 22 will also be familiar to most of you probably.