# 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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### showing that a matrix has repetitive values?

Here my primary aim is to calculate the stationary distribution of a DTMC using left-eigen values i.e, $\pi = \pi*P$. But for some matrices, I observe that some states a same stationary probability. ...
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### Testing the population mean

Given a population size and a sample, how can i test if the population mean is above a certain value? Similarly, can i find out what what value the sample mean has to be to say that the population ...
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### Weighted Standard Deviation for Histogram Bin Height

I'm plotting some binned data in the form of a histogram. Say I have 10 data points, each composed of a bin to be placed in, and then a "height". Then I might have something like: Bin Height 0 - ...
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### Calculating approximate growth from three numbers [closed]

I have a set of three numbers 3600, 5200,12000; how do I calculate an approximate 4th number ...
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### Correct statistic test(s) for resting energy expenditure (REE) vs estimated weightloss percentage (EWL)

Hello I am a student wanting to do a statistics test to compare the following: REE (initial) vs %EWL after one year. REE (initial) vs weight loss after one year. Change in REE (initial to one year) ...
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### How to create a fair dynamic scoring system? [closed]

I am currently in the process of creating a game consisting of a fixed set of tasks of varying difficulty. Each player gets the same set of tasks to choose from and is awarded a certain number of ...
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### find the maximum where gamma is attained

I have this problem and I am not figuring the beginning
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### Confidence interval for a density function parameter

I am trying to solve this problem: Given $X_1, \ldots, X_n$ a random sample of a population of random variables with p.d.f. $f(x, \theta) = e^{-(x-\theta)} I(x)_{x\geq\theta}$, find a confidence ...
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### Probability of getting n heads when n is very large [closed]

How to show that the probability of getting n heads when 2n times coin is toss is very small? Moreover, how to show that the probability of more than n heads is close to 0.5?
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### Use of language on wikipedia - what kind of distribution?

I have an interesting problem and was wondering whether anyone would be able to point me in the right direction. I am wondering whether the use of a word in the english language on Wikipedia is ...
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### Estimating a parameter using the maximum likelihood-method and the method of moments

Let $X$ be a random variable that has a density function of the form $f_X(x) = (p + 1) x^p 1_{[0, 1]}(x), x \in \mathbb{R}$ where $p > 0$ is an unknown parameter. I now want to make an educated "...
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### Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$

Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$, given that the autocorrelation of $x$ is: $$R_{xx} = \frac 1{n\pi}\sin\left(\frac {\pi}{2}n\right).$$ I've tried to ...
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### poisson process question.

The following calculations arise in certain highly simplified models of learning processes. Let $X_1(t)$ and $X_2(t)$ be independent poisson processes having parameters $\lambda_1$ and $\lambda_2$, ...
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### l1 regularization mathematical explanation

I somewhat understand what l1 regularization is, however, the mathematical formula and how to use it are confusing me. I'm not really sure what a regularization term is and how I could apply it to a ...
### Algebraic manipulation of normal, $\chi^2$ and Gamma probability distributions
If $X_1, \ldots, X_n \sim N(\mu, \sigma^2)$, then $$\frac{n - 1}{\sigma^2}S^2 \sim \chi^2_{n - 1}$$ where $S^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i^2- \bar{x})^2$, and there's a direct relationship ...