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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 →git · version-control · working-tree · staging-area · head · commit · branch · merge
打开 →backtest · backtest-engine · vectorized-backtest · event-driven-backtest · look-ahead-bias · point-in-time · engine-architecture · fill-simulator
打开 →factor-performance · realised-returns · headline-table · rolling-sharpe · regime-decomposition · ken-french · aqr · lsy
打开 →周二上午十一点。你的分支 feature/risk factor z 在本地终于跑通——沪深300 因子归因回测 Sharpe 三位小数都对上了审查者期望。你 git push ，在内网 GitLab 开了 MR，一小时内审查者要求改两处，并指出你的分支已落后 main 四个提交，因为同事刚合了另一个修同模块的 MR。第 1 课教你在一台机器上操作 git；...
打开 →某周五下午，深圳某 量化 私募 的 风控 周会。一位 研究员 端着一份 价值 动量 复合 策略 的 回测 报告 进 会议室：L1 都做对了——事件驱动 引擎、信号 计算 处处 .shift(1) 纪律。在 沪深300 成分股 上 2014 2023 回测，年化 夏普比率 1.3，曲线 干净、可上线。风控 总监 不问 信号本身 的 任何 一个 字，连珠炮 问了...
打开 →某周三 下午，上海 量化 私募 明汯 / 幻方 风格 的 投决会。研究员 上 来 一个 动量 策略：L1 引擎 是 事件驱动（干净）；L2 真实性 清单 每 一 项 都 过（PIT 数据、survivorship free 沪深300 股票池、下根 K 线 开盘 成交、双边 10 bps 成本、不 做 空）。报告 的 夏普比率 在 2014 2023 上 是...
打开 →周一早上 7:40,上海陆家嘴某头部私募的量化股票部。你按 4.3.1 走完了一套候选五因子模型——二维分组的十分位单调、Fama MacBeth 截面回归的斜率在样本内显著为正、按 HLZ 多重检验罚分调整后仍有可观利差。基金经理点了点头看完 IC 图,然后问出每一份研报必须先回答的那个问题:"好——但它真的 赚到钱 了吗?"4.3.1 给你的是因子构造的...
打开 →一位 五十亿 规模 私募 多 策略 基金 的 初级 研究员 周四 下午 走 进 代码 评审 室，端 着 一 个 看 起来 像 大 胜 的 信号 —— 中证 500 上 的 5 日 反转 策略，夏普 2.8，最 大 回撤 4%，2014 2023 年 区间 上 的 净 值 曲线 漂亮 得 不 像 话。资深 研究员 翻 着 notebook，问 了 一 个 问题...
打开 →周五下午四点。一家 A 股 私募 的基金经理走过来问：「昨天你跑的 沪深300 动量回测，能不能重现？早上 Sharpe 看起来不太对。」你打开 notebook，已经被改过两次——因子回看从 60 个交易日改成了 90 个，滑点假设也不知何时动过。没有 git 时你在靠记忆复原数字；有了 git， git log oneline 、 git checkou...
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?
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