Questions tagged [statistics]
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.
37,740 questions
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Is there a quicker way to solve this probability question?
Given:
There are three health risk factors, denoted by A, B, and C within a population of men. For each of these factors, there is probability .1 that a man in the population has only this risk factor ...
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How to use the binomial test for obtaining an accuracy threshold for a binary classifier?
Suppose that for each subject in an experiment, a classifier makes $n$ binary (correct/incorrect) predictions about that subject’s responses on a task. For a given subject, let $k$ be the number of ...
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The median of a frequency distribution and $g(x)=\sum_{k=1}^n f_k |x-x_k|$
My numerical experiments with several frequency data give rise to the following interesting features.
If a frequency distribution $(x_k,f_k), k\in [1,n]$ is written in ascending or descending order, ...
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Expectation under different laws
Suppose $X_1,\ldots,X_n$ are i.i.d. random variables generated from $\mathrm{Ber}(\theta_1)$. Then
$\mathbb{E}_{\theta_1}[\bar X] = \theta_1$, where the expectation is taken with respect to $\mathrm{...
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Need a review on my proof that a sequence forms a martingale [closed]
Condition of the problem
Let $\xi_1, \dots , \xi_n$ be independent identically distributed
random variables with finite mathematical expectation. Denote $S_k =
\xi_1 + \dots + \xi_k$ for $k = 1, \dots,...
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Question regarding independence in set theory: Does the provided statement give independence for one set of events, or all pairs of events?
Consider set H for Health insurance, and consider sets P as well as Q for life insurance (...
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Continuous vs Discrete Variables
How do I determine whether a statement or variable is discrete or continuous?
I am quite aware that discrete variables are those values that you can count while continuous are variables that you can ...
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Road map to probability and statistics regarding wildlife database [closed]
I am currently working in wildlife management, and I have some background in mathematics. I want to create a wildlife database with mathematical modelling in future. For that, I want to learn about ...
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Hypothesis testing with a sample from a shifted exponential distribution (Jun Shao - Mathematical Statistics, exercise 6.20, point (v))
Let ( $X_{1}, \ldots, X_{n}$ ) be a random sample from the exponential distribution on the interval ( $a, \infty$ ) with scale parameter $\theta$, where $a \in \mathbb{R}$ and $\theta>0$.Derive a ...
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Obtaining One of Multiple Subsets Coupon Collector Variant
Assume one draws from a standard deck of 52 cards with replacement and draws until they have seen at least one of each of the 13 cards from a suit (2, 3, ..., K, A). Whichever suit is fulfilled first ...
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What is probability distribution function of the sum of two independent random variables when one variable is correlated with itself?
Suppose we have the sum of random, independent variables
$$
Z_{ij} = X_i + Y_{ij},
$$
where $X_i \sim \text{Uniform}(-d, d)$ and $Y_{ij} \sim \text{Normal}(\mu, \sigma)$. Given that only one sample of ...
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Standard error of a mean direction
I have $n$ unit vectors $\mathbf{x}_i \in \mathbb{R}^p$, whose (sample) mean direction is calculated with
$$
\mu = \frac{\bar{\mathbf{x}}}{\bar{R}}, \text{ where } \bar{\mathbf{x}} = \frac{1}{n} \...
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Error distribution of linear Regression
Given the linear regression model
$$ Y = X\theta + \varepsilon, $$
the typical distribution of $\varepsilon$ is gaussian with mean zero and variance $\sigma^2$, but we could also assume $\varepsilon \...
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Finding an exact closed (non-recursive) form formula for the probabilities in a game of Risk
Yesterday I enjoyed some rounds of RISK: Global Domination with a friend from university. It is a long-running in-joke that “True Random” is the cause of winning and losing certain battles.
Our ...
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Double negatives in hypothesis test conclusions
I am grading hypothesis tests for an introductory statistics class and students occasionally give the following conclusion after rejecting the null hypothesis:
Since $H_0$ is rejected, there is not ...
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