题目4317 · 机器学习
Stacked CNN Receptive Field
A 1D CNN stacks 6 causal layers with kernel size 3, stride 1, and no dilation. What is the receptive field in tokens?
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中文题目题目1648 · 统计
Gaussian No-Intercept Regression as an MLE Problem
Suppose observations satisfy $$Y_i = \beta X_i + \varepsilon_i, \qquad \varepsilon_i\stackrel{iid}{\sim}N(0,\sigma^2),$$ with no intercept and known Gaussian errors. You are told that $$\sum X_iY_i = 48, \qquad \sum X_i^2 = 16.$$ Find the MLE of $\beta$.
打开 →题目358 · 概率
Law of Total Variance for a Poisson-Compounded Exponential Sum
Let $N \sim \operatorname{Poisson}(3)$ and, given $N = n$, let $S = X_1 + \cdots + X_n$ where $X_i \stackrel{\text{iid}}{\sim} \operatorname{Exp}(2)$ (rate 2). Using the law of total variance, find $\operatorname{Var}(S)$.
打开 →题目353 · 概率
Second Moment of a Random Sum via the Tower Property
Let $N \sim \operatorname{Poisson}(4)$ and, given $N = n$, let $S = X_1 + \cdots + X_n$ where $X_i \stackrel{\text{iid}}{\sim} \operatorname{Uniform}(0,1)$. Use the tower property and the identity $E[S^2 \mid N] = \operatorname{Var}(S \mid N) + (E[S \mid N])^2$ to find $E[S^2]$.
打开 →题目5720 · 脑筋急转弯
Sorting Pancakes by Spatula Flips
A stack of four pancakes has diameters, from top to bottom, $3,1,4,2$ (all distinct). The only allowed move is to insert a spatula under any pancake and flip the entire block above it, reversing the order of that top prefix. You want the pancakes sorted with the largest on the bo
打开 →题目5728 · 脑筋急转弯
Tower of Hanoi with Five Disks
Five disks of distinct sizes are stacked on the first of three pegs, largest at the bottom and smallest on top. You move disks one at a time from the top of any peg to the top of another peg, and a disk may never be placed on top of a smaller disk. What is the minimum number of s
打开 →题目2340 · 数理金融
XVA Desk Attribution Scenario 5
Why do desks usually discuss XVA as a stack of components when quoting and negotiating with clients, instead of presenting only one single all-in adjustment number?
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