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world:quiz4
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world:quiz4 [2025/10/03 01:38] rdouc |
world:quiz4 [2025/10/06 09:30] (current) rdouc |
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| - | {{Page>:defs}} | + | {{page>:defs}} |
| ====== Quiz 4 ====== | ====== Quiz 4 ====== | ||
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| Which of the following statements are true? | Which of the following statements are true? | ||
| - | * 1. Assume that $n=3$, the situation where we have $(h^2_{12},h^2_{13})=(0.2,0.2)$ is impossible. | + | * 1. Assume that $n=3$, the situation where we have $(h^2_{12},h^2_{13})=(0.2,0.2)$ is impossible. **TRUE** |
| - | * 2. The situation where $h_{ii}=0.5$, and for all $j\neq i$, $h_{ij}=0$ may happen sometimes. | + | * 2. The situation where $h_{ii}=0.5$, and for all $j\neq i$, $h_{ij}=0$ may happen sometimes. **FALSE** |
| - | * 3. If $\epsilon \sim N(0,\sigma^2 I_n)$ and if the (external) studentized residual $t_i^*$ satisfies $t_i^*<-2$, then we consider that $(x'_i,y_i)$ is a leverage point. | + | * 3. If $\epsilon \sim N(0,\sigma^2 I_n)$ and if the (external) studentized residual $t_i^*$ satisfies $t_i^*<-2$, then we consider that $(x'_i,y_i)$ is a leverage point. **FALSE** |
| ===== Exercise 2: Hoeffding's inequality ===== | ===== Exercise 2: Hoeffding's inequality ===== | ||
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| Let $(X_i)_{1\leq i \leq n}$ be iid random variables such that $\PP(X_1 \in [0,1])=1$. Which of the following statements are true? | Let $(X_i)_{1\leq i \leq n}$ be iid random variables such that $\PP(X_1 \in [0,1])=1$. Which of the following statements are true? | ||
| - | * 4. According to Hoeffding's inequality, $\PP\lr{\left|\frac{\sum_{i=1}^n X_i}{n} - \PE[X]\right| > \epsilon} \leq 2 \rme^{-2 \epsilon^2/n}$ | + | * 4. According to Hoeffding's inequality, $\PP\lr{\left|\frac{\sum_{i=1}^n X_i}{n} - \PE[X]\right| > \epsilon} \leq 2 \rme^{-2 \epsilon^2/n}$ **FALSE** |
| - | * 5. According to Hoeffding's inequality, $\PP\lr{\left|\frac{\sum_{i=1}^n X_i}{n} - \PE[X]\right| > \epsilon} \leq 2 \rme^{-2 n^2\epsilon^2}$ | + | * 5. According to Hoeffding's inequality, $\PP\lr{\left|\frac{\sum_{i=1}^n X_i}{n} - \PE[X]\right| > \epsilon} \leq 2 \rme^{-2 n^2\epsilon^2}$ **FALSE** |
| - | * 6. According to Hoeffding's inequality, $\PP\lr{\left|\sum_{i=1}^n (X_i - \PE[X])\right| > \epsilon} \leq 2 \rme^{-2 n\epsilon^2}$ | + | * 6. According to Hoeffding's inequality, $\PP\lr{\left|\sum_{i=1}^n (X_i - \PE[X])\right| > \epsilon} \leq 2 \rme^{-2 n\epsilon^2}$ **FALSE** |
world/quiz4.1759448307.txt.gz · Last modified: 2025/10/03 01:38 by rdouc
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