# 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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### Finding the frequency distribution function of a given compound distribution.

A random variable $N$ takes the values 0 , 1 and 2 with probabilities 0.5 , 0.25 and 0.25 respectively. We let $S = \sum X_i$ where $X_i's$ are independent and identically distributed random variables ...
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### Decomposition of Random Variable (Information)?

I am wondering whether the following idea or something similar appears in a field such as statistics or information theory(?). Take a random variable $Y$ which takes value $1$ or $2$ with equal ...
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### 1D random walk probability distribution

I am way more physicist than mathematician and this question arises from experimental physics/engineering. The motivation is dealing with small amount of random discrete shifts between measured ...
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### RMSE for shifted series

I am facing the problem to compare a series of simulations to a set of observations. Normally I would employ the Root Mean Square Error (RMSE) as goodness-of-fit measure to understand which is the ...
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### What at the chances of getting 20 heads on a row if tossed 100 million times? [duplicate]

I understand that each toss has a 50% chance if it is a fair coin, but I have hard time grasping the law of great numbers and I would like to know how likely it is that I get 20 heads in a row in such ...
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### Combine sum of binomially weighted Poisson distributions

I have the sum $$S(k,\lambda, n, p) = \sum_{m=0}^n P(k|m\lambda)B(m|n,p)$$ where $P(k|m\lambda)$ is a Poisson distribution with parameter $m\lambda$ and $B(m|n,p)$ is a binomial distribution with ...
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### What is the relationship between regression line and graph of averages?

Why is the regression line regarded as a smoothed version of the line of averages, and why is it that when the graph of averages falls on a straight line, that line is also the regression line?
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### the meaning and usuage of the variance of a discrete random variable

We know that the variance in continuous normal disturbed random variable, enable us to calculate confidence intervals. But I just have to wonder what is the point in calculating variance of a discrete ...
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### Why is the regression line an estimate of the average value of y for each value of x?

The regression line, passing through the point of averages with a slope equivalent to r, is said to be a good estimate of the average value of y for each value of x. I can see why this is the cases ...
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### what is the meaning of 'population' and 'sample' in statistics

In the context of finding the average weight of crows, the wikipedia article https://simple.wikipedia.org/wiki/Population_%28statistics%29 mentions that the 'population' is the set of measurements of ...
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### Summarizing set of parameters with different weights

I've an educational game which teaches several competencies sorted on relative difficulty in the ascending order. For each competency, I create challenges in the game, and during runtime following ...
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### Need help understand independent identically distributed random variable.

Let $X_1, X_2, X_3$ be three independent, identically distributed random variables each with density function $$f(x)= \begin{cases} 3x^2 & 0 \le x \le 1 \\ 0 & \text{otherwise} \end{cases}$$ ...
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### If Z has a normal distribution with mean 0 and variance $\sigma^{2}$, and $Y=Z^{2}$, what would the density function of Y be? [duplicate]

How would I go about finding this density function? Thanks
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### Exercises with solutions for mathematical statistics

I'm currently studying the statistics part of the book Georgii: Stochastics, contents are here (chapters 7 - 12). Sadly, there are no solutions for the exercises given in this book. Do you know a ...
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### Build skew normal distribution knowing the mean, max, and min

Say I have a data point with included errors and I want to build some continuous distribution around it. Normally this might be a Gaussian because one knows the sigma and mean right off the bat. ...
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### box and whiskers plot

I am having some troubles understanding what the components of a box and whiskers plot mean. Let's say I have some observations. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ...
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### explain why accounting data follows Benford's law

I've spent a lot of time recently investigating on Benford's law. Many sources state that Benford's law can be useful when auditing accounting data. Non-fraudulent accounting data (under "good" terms) ...
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### sufficient statistics to estimate the unknown parameters

I am a beginner in statistical inference and am learning sufficient statistics. As far as I know the distributions conditional on the sufficient statistics doesn't depend on the unknown parameters. I ...
We have 2 independent random variables $a \sim N(0,1)$ and $b \sim N(0,1)$. I want a proof (or even good intuition) to show that the chance of having the pair $(a_0,b_0)$ is a function of only the ...