# 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.

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### How objectively do we evaluate likelihood of two very rare events?

I've been pondering the concept of objectiveness to evaluate likelihood and predictability of extremely rare events. I'd like to demonstrate my questions over trivial hypothethical examples below. ...
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### Binomial: normal approximation

I am having the hardest time coming up with the standard deviation that textbook is coming up with. Suppose 14% of the U.S. population is left-handed. If a random sample of 200 people from the U. S. ...
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### Probability of someone in a given sized group, given their prevalence in the larger population

I’m sure my title was a terrible description of this question. On twitter, @BobWachter posted this: Asymptomatic test pos. rate @UCSFHospitals now 6.2%. That's 1-in-16 w/ no symptoms of Covid who test ...
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### Why is this independent random variable cannot deduce $\mathbb{E}(Y^2)=\mathbb{E}(Y)\mathbb{E}(Y)$

Here is the proof of biased and unbiased sample variance. Since they are random sample they are i.i.d. From the process of $$\sum^n_{i=1}\mathbb{E}(Y^2_i)-n\mathbb{E}(\bar{Y}^2)$$ I was thinking about ...
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### Deriving estimators for functions of an unknown parameter $\theta$

I am wondering if there is an easier way to find an estimator of a function of an unknown parameter $\theta$ for a particular statistical model. For example, if I derive the Maximum Likelihood ...
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### Consistent estimator of function of moments up to given order

Asume we the moments of a distribution exist up to order $n$. Consider the estimator $$t (x)=f(m_1(x),..., m_n(x))$$ where $m_k(x):=1/r \sum_{i=1}^r x^k$. We assume we have $r$ samples of the ...
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### preventing rare extreme values in linear regression prediction

I am trying to train a model with a lot of input variables using linear regression. For technical reasons, my training data is obtained from a simulation that closely but not perfectly mirrors the ...
1 vote
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### TF2 crithack detection via statistical analysis

This is a idea that I've been thinking about for quite some time, but I'm not good enough at statistics to work out how to do it. Sorry in advance. I don't plan to implement this, but feel free to ...
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### Can we calculate the opponent's hidden values in this statistical battle?

First-order statistical battle Imagine there is a game in which the user should guess what values the opponent is hiding from the user. In the first battle, the opponent has two hidden values ...
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### Calculating a sample size

I can't figure out how to crack this problem. It's as if I don't have enough information. Walk me through please Jogging is a popular sport in Brilliantia. According to a recent survey, between 80% ...