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.

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Why are there two different versions of the mean and variance for negative binomial distributions

On a wiki proof site, I've seen these formulas used for the mean and variance: $E[X] = \frac{rp}{1-p}$ and $Var[X] = \frac{rp}{(1-p)^2}$. Yet on the Penn State site, they have these two different formulas: $E[X] = \frac{r}{p}$ and $Var[X] =…
Mark Jizelle
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Calculating success chance from algorithm

Not super sure this is the right *exchange for this question, but here we go. Let's say I'm writing a game, and in this game the player may attack another unit. The chance of hitting is an "opposed roll" that looks something like this: An attack…
Jonatan Hedborg
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Why are these estimates to the German tank problem different?

Suppose that I observe $k=4$ tanks with serial numbers $2,6,7,14$. What is the best estimate for the total number of tanks $n$? I assume the observations are drawn from a discrete uniform distribution with the interval $[1,n]$. I know that for a…
rjt90
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Statistics formula for wifi positioning.

Assuming I have $3$ access point namely: $AC_1$, $AC_2$ and $AC_3$ and I want to know my location using this access point and a mobile device that will get signal from the access points. First thing that I did is save the signal level for different…
Hope
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I'm trying to understand the following derivation

This is taken from Hastie, Tibshirani and Friedman's Elements of Statistical Learning. They describe the squared loss error and to minimize the expectation of this error, which they call Expected (squared) prediction error, $EPE$. They first define…
brewberry234
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In the definition of a complete statistic, what is the expectation taken over?

I have read lots of answers here attempting (and in my case, failing) to convey the idea of a "complete statistic." Even the idea of $E_{\theta}[g(T(x))] = 0$ is hard to parse. What is the expectation taken over? Different data? Different values…
RobertTheTutor
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Statistical Odds calculation for a video game occurrence

In a video game I'm playing, there is a random number generator that awards one trophy from a pool of possible trophies. The pool of possible trophies is approximately 60 different items, and I was supposed to be awarded 5 random ones. I received…
software evolved
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Can Fisher Information be negative?

Can $$I(\theta) = -E\left[\frac{\partial^2}{\partial\theta^2} \ln f(x,\theta)\right] = 0$$ I've heard that Fisher's Information is strictly greater than zero but I'm unsure why. A proof would be much appreciated!
rookie
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what is the median of the CDF with the form $F(x) = 1 - e^{-(x/3)^2}$, for $x \gt 0$

Consider The distribution of lifetimes, X(in months), of a particular type of component. The Cumulative distribution function (CDF) has the form $$F(x)=\begin{cases} 1 - e^{-(x/3)^2},& \text{if} ~ x \gt…
Ria
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Usefulness of Variance

I've had a look for intuitive explanations of the variance of an RV (e.g. Intuitive explanation of variance and moment in Probability) but unfortunately for me, I still don't feel comfortable with the concept. Why would you opt to use variance over…
atem
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Finding the MVUE using Rao-Blackwell Theorem

The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean $\lambda$. The daily cost of repairing these break downs is given by $C=3Y^2$ If $Y_1, Y_2, ..., Y_n$ denote the observed number of breakdowns for $n$…
math101
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Expectation and variance of top 10% of any normal distribution

Short: With the standard curve (i.e. mean=0, std dev=1), does the top 10% form its own normal distribution with the expectation about 1.74 and the standard deviation about .40? Long: I wrote a little program that takes the numbers…
midmath
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Variance of $\overline{X}_n^2$

Here is a problem a have got in my homework. Given a set of $X_1, ... X_n \sim F$ i.i.d values find the variance of $T_n = \overline{X}_n^2$ where $\overline{X}_n = \frac{\sum_i{X_i}}{n}$. I actualy have an answer for this problem: $V(T_n) = \frac{4…
alexanderkuk
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Working out minimum sample size

I have just started a course in statistics and have some general questions that have arisen trying to solve the following question: A survey organisation wants to take a simple random sample in order to estimate the percentage of people who have…
Ben
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Addition Rule for Expectations

Why does the addition rule for expectations work no matter if the sub-events involved is independent or dependent? For example: Let $X$ be the number of aces in a 5-card poker hand. The probability that any particular card is an ace is…
A_for_ Abacus
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