All Questions
4 questions
28
votes
3
answers
4k
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Confidence Interval for variance given one observation
This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":
Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters unknown, ...
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14
votes
2
answers
6k
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Variance of maximum of Gaussian random variables
Given random variables $X_1,X_2, \cdots, X_n$ sampled iid from $\sim \mathcal{N}(0, \sigma^2)$, define
$$Z = \max_{i \in \{1,2,\cdots, n \}} X_i$$
We have that $\mathbb{E}[Z] \le \sigma \sqrt{2 \log ...
- 689
14
votes
4
answers
6k
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Meaning of "Overdispersion" in Statistics
I am trying to understand what "overdispersion" means in statistics.
Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is ...
5
votes
1
answer
3k
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How do we derive that $S^2$ is chi-squared distributed (with $n-1$ df)?
The claim is that $$(n-1)S^2/\sigma^2$$ is chi squared distributed with degrees of freedom $n-1$.
$(n-1)S^2/\sigma^2$ can be written as $$\sum_i^n \left(\frac {x_i-\mu}{\sigma}\right)^2-\left(\frac {...
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