# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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### Calculating success chance from algorithm

Not super sure this is the right *exchange for this question, but here we go. Let's say I'm writing a game, and in this game the player may attack another unit. The chance of hitting is an "opposed ...
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### Regarding probability bound of flip coins

Suppose you flip a fair coin 10,000 time how can you characterize the distribution of the occurrence of head? From the textbook, it says that $P[head>\frac{n}2 + k\sqrt{n}]$ < $e^{-{k^2/2}}$, ...
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### How to find the best fit when you have a set of ideal ratios, but some of those are below a minimum?

Say you have a set of ideal ratios, whose sum = 1. For example, input = [0.2, 0.2, 0.3, 0.3] But suppose that there is a rule stating that every ratio should be ...
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### Minimization values for a function [duplicate]

I have got function - non linear(I thk), and a set of variable S=[(x1,y1),(x2,y2)...]. The objective is to find the value for ...
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### Statistics: Why do we divide by $\sqrt{n}$ for sample standard deviation

Can someone tell me if my explanations/understanding is on the right track? Suppose we have a set of variances, each of them identical, where $V_{1}(x) + V_{2}(x) + ...+ V_{j}(x) = \sigma^2$. If we ...
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### Probability of Specific event occuring between 2 events?

Forgive me beforehand for what may be a question with an obvious seolution, but I havent had statistics courses in quite some time. I have an Excel File of approximately 3000 Events, each event has a ...
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### Chi square proof with Exp law

For an exercice in Statistics, For $X \sim Exp(\theta)$ I have to proof that : $(\dfrac{2} {\theta}) \sum_{i=1}^{12} X_i \sim X^2(24)$ And with this result, I have to found a best critic ...
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### data interpretation

let us consider following picture and question: INCOME: 1. Money from fund raising programmes, 2. Grant from the government, 3. Contributions from individuals, 4. Contributions from corporations, ...
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### Expected number of draws to draw a unique item given outcome probability distribution with replacement

Given a mystery box with multiple outcomes, if the outcome of concern has a probability of being drawn with 15%, what is the expected number of draws to draw this outcome? Can we assign a dollar ...
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### Where did this statistics formula come from: $E[X^2] = \mu^2 + \sigma^2$

I am studying statistics and I need some guidance as to where this formula came from. All I know is that $\displaystyle E[X^2] = x^2 \sum_{i=0}^n p_{i}(x)$
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### (theoretical) Negative Binomial Distribution using Matlab

I was trying to solve some exercises on Matlab in order to improve my skills and I stumbled upon this question: For the (theoretical) Negative Binomial distribution with parameters r = 5, p = 0.4, ...
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### Distribution of the $l_2$-norm of gaussian vector

Let $Y_k \sim N(\mu_k, \sigma_k^2)$. For $\sigma_k = \sigma$ the squared norm of $Y = (Y_1, \ldots, Y_n)$ follows the noncentral chi square distribution. What is the distribution in the general case? ...
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### Why the definition of Variance is such. [duplicate]

Why we define the variance of a random variable $X$ as $\text{var}[X]=\text{E}[(X-\mu)^2]$ instead of $\text{var}[X]=\text{E}[\left|X-\mu\right|]$. Normally we understand the standard deviation ...
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### Statistical Significance level - elementary level

Let's say one day my sister tells me she has psychic powers and can help me predict the winners in horse racing games and for whatever reason, we only have 2 horse racers in a game. She tells me that ...
Edited for the sake of clarity: If you have a random variable $Q$ distributed uniformly on some interval, say $[a,b]$, what is the function $f$ that describes how many times you have to draw on the ...