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 would I solve this poker statistics question with an infinite deck?

My professor threw out this question for the class as an extra credit question. I'm not asking for an answer, but rather, a nudge in the right direction to solve the problem. I'm currently stuck because this question is not discrete because it…
user2837858
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Incorrect calculation? (Statistics homework)

I'm currently working on some statistics homework, and as you might guess from the title, I got the wrong result, and the reason why I'm writing it here is because I don't have a clue why it's wrong. The question is as follows: A student is driving…
Nikolaj Kyed
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Is there a convenient formula for variance of discrete random variable in terms of CDF

For a discrete random variable X, $\Omega_X\subseteq \{0,1,2,\ldots\}$, we can write $$\mathrm{E}[X] = \sum_{x=0}^\infty (1-F(x)) $$ where $F(x)$ is the cumulative distribution function of $X$. This formula is proving convenient to me on the current…
TooTone
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Is it possible to obtain Cov(X,Y) from only Var(X) and Var(Y)?

Am trying to write a simple program that can take an arbitrary data-set of [x,y] pairs from given file, analyzes and prints any interesting statistical characteristics. Of the things am interested in, is printing some statistical description of the…
JWL
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Non-technical question about maximum likelihood estimation / intuition

Just a quick question on MLE, sorry if its too basic but I would love help on this issue! If we want to calculate the probability $P$ of the number of males in the United States and we knew the distribution $pmf$/$pdf$, why can't we just take the…
nicefella
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Grouped data median, using lower class limit or lower class boundary?

In statistics, for grouped data, when calculating the median based on formula $Median = L_m + \left [ \frac { \frac{n}{2} - F_{m-1} }{f_m} \right ] \times c$ where $c$ is the size of the median class $F_{m-1}$ is the cumulative frequency of the…
Allen
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Calculating interquartile range

I have the following numbers: $$\{0, 1, 2, 5, 8, 8, 9, 10, 12, 14, 18, 20, 21, 23, 25, 27, 34, 43\}$$ and need to calculate the IQR. My calculations gave…
Carlos
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How to show that estimator is unbiased

Let $f(x;\theta) = (1/\theta)x^{(1-\theta)/\theta} $$\hspace{20 mm}$ $ 0
brian
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How to prove something is a sufficient statistic?

If you have $n$ random variables that are iid with density $\frac{1}{p}e^{-x/p}$, how do you show that the sum of the $x_i$'s is a sufficient statistic? Attempt: Take likelihood function and express in terms of $g(p)h(x)$ and use factorization…
lord12
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Quantile density function: student's t vs normal

I'm trying to show that $\frac{\exp\Big(\frac{\Phi^{-1}(x)^2}{2}\Big)}{\Big(1+\frac{\Psi^{-1}(x)^2}{\delta}\Big)^{(\delta-1)/2}}$ goes to infinity as $x$ goes to one, where $\Phi^{-1}$ denotes the inverse CDF of the standard normal, and $\Psi^{-1}$…
Rob
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The sum of Gaussian functions

Suppose there is a normal distribution and the Gaussian function is $F(x)=\exp(-c\|x-b\|^2)$ where $c$ is a constant and $x,b\in \mathbb{R}^N$, b means the mean value.…
Vivian
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Statistics question: appropriate test of significance?

The following question came to mind while I was playing tennis. Even when I'm taking a break, I can't turn the math brain off. I'm sure this is a simple question for the statisticians here. Say a tennis player wins 100 out of 200 points in a match.…
Nick D.
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Distribution of $(XY)^Z$

Can you please help me with this. Let $X,Y,Z$ are independent random variables uniformly distributed over $[0,1]$. Show that $(XY)^Z$ is also uniformly distributed over $[0,1]$ I try to show that $-Z(\ln X+\ln Y)$ has an exponential distribution,…
user115124
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Where do the definitions in statistics come from?

The most statistics I ever took was a few lessons on it back in high school. What always bothered me is how arbitrary the definitions seemed. For instance, I remember having trouble with the definition of standard deviation. The standard deviation…
Jack M
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Find minimal sufficient statistics and ML estimator

Let $X_1, X_2, \ldots, X_n$ be i.i.d. uniform $(a-b, a+b)$, where $b>0$ and let $\theta = (a,b)$. Find a minimal sufficient statistics $t$ for $\theta$. Find the ML estimator $\hat{\theta}$ of $\theta$. So, what I have done is for minimal…
ssandi
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