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中文题目Let $X \sim \operatorname{Exp}(\lambda)$ and $Y \sim \operatorname{Exp}(\mu)$ be independent. Player A finishes at time $X$ and player B finishes at time $Y + c$ where $c > 0$ is a head start for player A (player B starts $c$ time units later). (a) Derive $P(X < Y + c)$ — the pr
打开 →You flip 3 fair coins and independently roll a single fair six-sided die. What is the probability that the number of heads strictly exceeds the value shown on the die?
打开 →A daily factor is z-scored using the full-sample mean and standard deviation before the backtest is run. What is the main problem?
打开 →A backtest ranks stocks each month using the latest fully restated accounting data available today, even for years long ago. What is wrong with that setup?
打开 →A research notebook chooses the top decile each day using today's close and then records the same day's close-to-close return as PnL. What is the leak?
打开 →A training set includes observations whose labels use returns that overlap with the future test window. What should be added to the split procedure?
打开 →A PM wants to backfill today's index membership list into the whole historical universe before evaluating a factor. Why is that unsafe?
打开 →You flip 3 fair coins. What is the probability that at least one coin lands heads?
打开 →You flip 4 fair coins. What is the probability that exactly 2 of them land heads?
打开 →A fair coin is tossed $100$ times. Compare the Hoeffding and Chebyshev upper bounds on the event that the fraction of heads is at least $0.65$.
打开 →You flip 6 fair coins in sequence. What is the probability that no two consecutive coins land heads?
打开 →You flip a fair coin $n$ times independently. A transition at position $i$ (for $1 \le i \le n-1$) occurs when flip $i$ and flip $i+1$ differ (one is heads and the other tails). Find the expected number of transitions. Additional robustness twist: before observation, an independ
打开 →You flip 8 fair coins. What is the probability that somewhere in the sequence there is a run of at least 3 consecutive heads?
打开 →You flip 5 fair coins simultaneously. What is the probability of getting exactly 3 heads?
打开 →For a GARCH(1,1) process with $\omega=1$, $\alpha=\frac{1}{10}$, $\beta=\frac{4}{5}$, suppose you already know the one-step-ahead conditional variance $h_{t+1}=5$. Compute $E_t[h_{t+2}]$ and $E_t[h_{t+3}]$.
打开 →Aggressive and passive child orders fill as independent Poisson processes with rates $\lambda_A=10$ and $\lambda_B=5$ per minute. What is the probability that the first three fills in the merged stream are all aggressive (stream A)?
打开 →In a branching process, let the offspring distribution have variance $\sigma^2$. Express \[ \mathrm{Var}(Z_{n+1}\mid Z_n) \] in terms of $Z_n$.
打开 →7 people sit in a circle, each wearing a hat colored red, green, or blue (assigned independently and arbitrarily). Everyone sees all hats except their own. They must all SIMULTANEOUSLY write down a guess of their own hat color (no information exchange after seeing the hats). They
打开 →A fair coin is flipped repeatedly. What is the expected number of flips until the pattern $HHH$ first appears?
打开 →Before adding a new return-based feature to your model, what is the first alignment question you should ask?
打开 →What should you check first before lengthening a forward-return horizon because the 1-day target looks noisy?
打开 →What should you clarify before residualizing returns against factors and treating the residual as a new feature?
打开 →Before standardizing a return feature, what should you check about the universe you are mixing?
打开 →A return feature looks very important in a trained model. What should you check first before concluding it captures genuine alpha?
打开 →You predict tomorrow's close-to-close return at today's close, but one feature uses today's official closing auction price finalized after the decision timestamp. Why is that a leakage problem?
打开 →A feature uses raw prices while the target uses split-adjusted future returns. What problem can that create?
打开 →Why should factor residualization for a daily return feature use exposures known at the feature timestamp rather than exposures estimated using later returns?
打开 →You test 40 independent noise strategies. A strategy is launched only if it passes an in-sample screen at level 1/20 and then passes a second independent validation at level 1/10. Under the global null, what is the probability that at least one noise strategy still gets launched?
打开 →A signal becomes public at Tuesday 4:15pm ET. A daily strategy may only trade after all input data are known. What is the earliest tradable session?
打开 →A signal becomes public at Wednesday 8:10am ET. A daily strategy may only trade after all input data are known. What is the earliest tradable session?
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