Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, 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 mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
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How to calculate correlation between poll statistics and one's answers?

I have statistics of $100$ questions which can be answered either "yes" or "no": 1) $63.3 - 36.7$ ($63.3\%$ respondents answered "yes" and $36.7\%$ answered "no") 2) $30.1 - 69.9$ ... 100) $88.0 - 12.0$ That $100$ answers would be our sample. Then I…
Stanislav Shabalin
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Monte-Carlo method

I have a problem with my statistics task. It sounds like this: "Using the Monte Carlo method, plot the dependence of a on b for a from -5 to 5, where $P (a < x-y < b) = 0.95$, where $x\sim N(0,1)$, and y is a uniformly distributed random variable…
user515149
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Making conclusions from data with mixed up labels?

We have a question which asks something strange, something which seems like it would prevent any conclusions being made from the data. The question is as follows: The subjects of a study came from a genetically pure strain of rats. From each…
Helen Peters
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Kolmogorov–Smirnov 2-sample test with large sample sizes always significant

I'm aware that the probability of a traditional statistical test such as student's t or mann-whitney u being deemed significant approaches 1.0 as sample size increases (i.e. >10,000) but I'm getting the same issue with a Kolmogorov–Smirnov 2-sample…
G Warner
  • 121
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Joint probability density function and limits of integration

Suppose we have $f(x,y) = 2$ when $x>0$, $y>0$, $x+y <1$ and $0$ elsewhere. I want to find the $\Pr(Y>X)$ and I'm struggling with finding the correct limits of integration generally but especially when we want to find $\Pr(Y>X)$ or similar. Can…
user496975
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Marginal probability density function of joint pdf

Let X has a uniform distribution on the interval (0,1). Given that X=x, Y has a uniform distribution on the interval (0,x). Find the marginal p.d.f. of Y. My thought: marginal pdf…
user227158
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What if the relative error is undefined?

The relative error is defined by the simple formula: $$\text{Rel. Error} = \frac{|v_\text{approx}-v_\text{analytical}|}{v_\text{analytical}}$$ but what if the theoretical value $v_\text{analytical}$ should be $0$? then our relative error is…
user32882
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How to fit fixed data from two linear functions

I have a set of points $(x, y)$ where each one comes from either one of two linear functions: \begin{align*} y &= m_1 x + b_1\\ y &= m_2 x + b_2 \end{align*} Is there a fitting method to find such functions, without knowing from which…
Hernan
  • 123
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Generating a list of numbers whose combinations are mathematically unique

I'm trying to design a puzzle for a game I'm making, and the puzzle is fairly similar to the one from the power plant in Myst. The idea is that I have 9 buttons, and each button supplies an amount of power to the "system". The solution to the puzzle…
Abion47
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Show a statistic is complete but not suffcient

Let $X_1, ...,X_n$$(n \geq 2)$ be i.i.d. random variables having the normal distribution $N(\theta, 2)$ when $\theta = 0$ and the normal distribution $N(\theta, 1)$ when $θ ∈ R$ and $θ \neq 0$. Show that the sample mean $\bar X$ is a…
Ma Xingkong
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How to test null hypothesis for spatial distribution?

I am given a sample from a spatial distribution $X$. For example, my variable $X$ is the number of certain diseases per city per capita. Null hypothesis is that variable $X$ does not depend on the location directly (it might be dependent on another…
Andrei Shamis
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Sample variance of rolling a die 100 times

The textbook gives an example of testing a null hypothesis that rolling a die 100 times will give you a value of $6$, $\frac{1}{6}$ times. In the experiment, a die was rolled 100 times and 30 of them were $6$'s. The book obtains a $z$ score for this…
CodyBugstein
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If 9 people play against each other twice for one point each, what is the minimum number of points you would need to be guaranteed in the top 6?

If 9 people were going to play a game against each other, two times each (each game would be 1 point), how many points would an individual person need to get to be guaranteed to be in the top 6? I am trying to figure out the magic number for a…
Jacob Malachowski
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Is there an easy way to (mentally) sum i.i.d. discrete uniform random variables?

I was recently trying to do some mental mathematics and found myself stumped when trying to handle what ought to be a simple problem. My issues essentially boiled down to the question that I've asked, although for the sake of making the numbers easy…
J. Min
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Numerics for Tracy-Widom distribution

I have data for a random variable and I wish to test whether it conforms to the Tracy-Widom distribution. However, the T-W distribution is hard to compute. Is there a readly available table of its values I can just download?
Marcel
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