# 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.

2,485 questions
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### Cake slicing hypothesis problem

A cake weighing one kilogram is cut into two pieces, and each piece is weighed separately. Denote the measured weights of the two pieces by $X$ and $Y$ . Assume that the errors in obtaining $X$ and $Y$...
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### Find an estimator of $N$ (hypergeometric)

A forest has $N$ (unknown) monkeys. A random sample of $n$ monkeys is selected from the forest, tagged and released back into the forest. After a few days, a random sample of $m$ monkeys is selected ...
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### 1D Bayesian Inference clarification

I'd like some help making sure I understand a 1D Bayesian inference problem. Stats.stackexchange wasn't helpful. Say I have a data vector which is an array of the number of flu cases reported weekly ...
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### Are there generalised rules for generating heuristics from data?

Heuristics seems to be more of an art than a science, like a gut-feel supported by data; I might be wrong. Are there algorithms for mathematically generating heuristics from data, like pruning a ...
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### Karlin Rubin Theorem UMP (Uniformly most powerful test ) Is it wrong?

Suppose $X_1, X_2, X_3,\ldots, X_n$ are i.i.d. random variables with a common Poisson$(\lambda)$ distribution. $$X=(X_1, X_2, X_3,\ldots, X_n)$$ and $g(λ)=\lambda(1 - e^{-λ})$ , with $(λ>0)$ ...
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### What is the value of the likelihood ratio test statistic for a given poisson distribution?

In past weeks, the average number of life insurance policies sold per week was $θ = 3$. However, this week he has sold 6 life insurance policies. Based on this single observation of $x = 6$, what is ...
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### How does one represent an econometric model? (an application of the ergodic theorem to stationary time series).

THE FRAMEWORK: Let $X_1 , X_2 , \dots, X_n$ be observed random variables. Then one could decide to model them as IID Gaussians with variance one and mean $\mu$. That is we choose as our model the ...
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### Why is the bottom limit of the conditional probability $x$ in Bayesian Statistics?

I am learning bayesian statistics and was stuck when trying to understand the following example: Romeo and Juliet start dating, but Juliet will be late on any date by a random amount X, uniformly ...
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### Sufficient statistic for Double Exponential

Let $X_1,X_2,...X_n$ be a random sample from $f(x,\theta)=\frac{1}{2 \theta}e^{\frac{-|x|}{\theta}}$.We know by Factorisation theorem that $\frac{\sum |X_i|}{n}$ is sufficient for $\theta$. But can ...
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### Find the maximum likelihood estimator for Pareto distribution and a unbiased estimator

Let $X_1,...X_n$ be a random sample from the Pareto distribution with parameters $\alpha$ and $\theta$, where $\alpha$ is known. Find the maximum likelihood estimator for $\theta$ and say if it is ...
Are linear combinations of independent normally distributed random variables also independent? Suppose we have two independent standard normal variables $X\sim N(0,1)$, $Y\sim N(0,1)$. Let $U=X+Y$ and ...