# Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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### How are category theory and probability theory related?

How are category theory and probability theory related ? Category theory seems very useful for understanding objects with definite relationships, whereas probability theory (particular Bayesian ...
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### Going Through Yellows

I have observed that I am almost never the last car through a traffic light. Sometimes I stop (because it is yellow or red), in which case, of course, the car behind me also stops and the car in front ...
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### Find a function such that follows to normal in distribution

Suppose that $X_{n}\sim \text{Binomial}(n,\theta)$, where $n=1,2,\ldots$ and $0<\theta<1$. Find a function $g$ such that $\sqrt{n}(g(\frac{1}{n}X_n)-g(\theta))\xrightarrow{D} N(0,1)$ for each ...
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### Proof of Theorem 4.16 from Mathematical Statistics by Jun Shao (Second Edition, Section 4.5.1, p.287)

First I would like to state the Theorem - it reads as follows: Let $X_{1}, \dotsc, X_{n}$ be i.i.d. from a p.d.f. $f_{\theta}$ w.r.t. a $\sigma$-finite measure $\nu$ on $(\mathcal{R},\mathcal{B})$ ...
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### Bayesian hypothesis testing and posterior distribution

Let $X$ be a random variable with a probability density $f(\cdot;\theta)$ where $\theta \in \Theta \subset \mathbb R$ is an unknown parameter. Suppose that we have a prior density $\pi(\theta)$, with ...
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Let $X_1, \dots, X_n$ be a random sample from a Poisson population with parameter $\lambda$ and define $Y = \sum_i X_i$. Y is sufficient for $\lambda$ and $Y \text{~} \text{Poisson}(n \lambda)$. ...