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.

25,264 questions
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Mean and covariance of this stochastic process

We have a process $$x(t) = \text{atan} (cB(t) + \tan (x(0))),$$ where $c$ is a positive constant, $B(t)$ is a standard Brownian motion, and initial value $x(0)=1$. How to analytically calculate ...
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Expected values of expected values when using sample statistics

Econometrics class was teaching properties of expected values and showing how they were used in some proofs. I decided to try and proof the variance formula for the variable W [e.g. W=aX+bY] and ran ...
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Good test statistic

If we have a hypothesis $H_0$ and alternative hypothesis $H_1$, a test statistic $T$ and a data set $x_1, ..., x_n$ taken from some random sample $X_1, ..., X_n$, we use $T(x_1, ..., x_n) = t$ to ...
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standard deviation for proportion with huge denominator

My question involves finding the standard deviation of a ratio when the denominator is huge. The standard formula $\sqrt{(p*(1-p)/n)}$ yields a number that is almost zero. The context is computing a ...
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What is the explanation of Average Variance Extracted in expression f(x) = Ave(y(i)|x(i)∈Nk(x))?

Wikipedia defines it as: average variance extracted (AVE) is a measure of the amount of variance that is captured by a construct in relation to the amount of variance due to measurement error. At my ...
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Need Help for Solutions Manual

I am trying to solve all the exercise problems in the book "understanding machine learning: from theory to practice". I am doing so because there is no available solution manual, and the book is such ...
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Transformation of Wishart distribution

I am a bit confused about transformations of matrix distributions. Say, I have a $n \times n$ matrix $\Sigma$ which has a Wishart distribution $W_n(\Phi^{-1}, n+1)$, so that its p.d.f. is ...
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Is the mean or median a better measure of central tendency?

I was given this question by my friend who said he got it from his teacher (which meant he couldn't clarify the terms in this question). The question is: What is a better measure of central tendency? ...
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Reduction in mean associated with p-value

I was reading a paper and they reported a mean reduction in parameter $1$ of $5.2\% (p=0.07)$ and a mean reduction in parameter $2$ of $10.7\% (p=0.12)$. Can this be correct? I thought that the ...
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Distribution function technique and exponential density

I'm having quite a bit of difficulty with the distribution function technique. If $X_1$ and $X_2$ are independent random variables having exponential densities with parameter $\theta_1$ and $\theta_2$...
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Having trouble with given task [on hold]

The random size is distributed according to the normal law, which is an average of 15. Calculate this random size dispersion if it is known that the probability of gaining values ​​from the range [15; ...
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Sample Space & Combinations/Permutations

This is the question: "List the sample space for three individuals chosen at random to vote either Democrat or Republican. List the distinct combinations and permutations." These are what I got for ...
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How to combine a number frequency data set into tradional lottery number calculation?

I'm trying to figure out how to combine historical lottery data with a traditional lottery number probability calculation technique to result in a more "accurate" probability of a number being drawn, ...
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Conditional Probability in Geometric Distribution

Ms. A is taking driving test to get her driving license. The probability of passing a test is 0.3 which remains same no matter how many times she takes the test. Let $X$ is a random variable which ...