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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Doubt about exponential distribution

I'm given a certain seed number, lambda and k number of observations. I'm suppossed to find sum(k), divide it in unit intervals, check how many events occured in each interval, calculate the mean of events and finally calculate the absolute…
Anon
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How to find the probability of the largest $k$ values from $n$ sorted stacks being in the top $m$ items from each stack?

Let’s say I have a set $U$ containing some values. I randomly distribute these values into $n$ stacks and sort each stack from largest to smallest. Then I take the top $m$ items from each stack to form a set $S$. What is the probability the largest…
Cameron Toy
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How to calculate relative performance (non-finance) when lower is better?

Example: Car 1 goes from 0-60 in 6 seconds. Car 2 goes from 0-60 in 8 seconds. Car 3 goes from 0-60 in 9 seconds. Now, Car 1 is obviously the fastest, so I want to make it my reference and express other cars' performance relative to it. If higher…
Blake Bringer
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Statistics Confidence Intervals

True or false: a) The center of a 95% CI for the population mean is a random variable? d) Out of 100 95% CI for the mean $\mu$, 95 will contain the mean $\mu$?
mary
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Poisson random variable with parameter lambda~uniform(0, 10)

Suppose $N\sim Poisson(\lambda)$ and $\lambda\sim Unif(0, 10)$ what is the expected value $E(N)$? I feel like I should just plug in the expected value of Unif(0, 10) but that seems too easy. Anyone have any thoughts?
Deddryk
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Methods for determining thresholds for future use based on historical data (in R or Excel)

Let's say I have some data about the amounts of reports to Help Desk (about technical problems) which were monitored and registered every five minutes for the whole day (even during the night). Is there any way to efficiently calculate the…
Luxy
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Statistical Significance level - elementary level

Let's say one day my sister tells me she has psychic powers and can help me predict the winners in horse racing games and for whatever reason, we only have 2 horse racers in a game. She tells me that if she chooses 'blue', then the blue horse wins…
Lemon
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expected value in Poisson distribution

E(X) in Poisson Dist, \begin{align} \mathrm{E}(X) &= \sum_{k=0}^{\infty} \frac{k \lambda^k e^{-\lambda}}{k!}= \\ &= e^{-\lambda} \sum_{k=0}^{\infty} \frac{\lambda^{k+1}}{k!}=\\ &= \lambda \end{align} then, $\text{E}(X(X-1)) = \sum_{k=0}^{\infty}…
Levy
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What are some recommended Rating Systems for a Single-Elimination Bracket Tournament?

I have gathered data on a set of certain contests. The contests are in the form of single-elimination. That is, there are $2^n$ competitors in $n$ rounds. In each game, two players face each other, and the loser gets eliminated, until only one…
S_H_
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Frequency $\times $ Midpoint = What?

When finding the mean of grouped data, at some point you need to do: Frequency $\times $ Midpoint = ..... Could someone tell me the name of the answer, does it have a name? Its labeled as fx in a lot of places, but I don't actually know what to call…
Jamie
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How can I compute my final grade?

In one of my courses in the university, I got: Final: (93 out of 100) [25% of the course] 2nd Major: (100 out of 100 + bouns 1) [12.5% of the course] 1st Major: (93 out of 100) [12.5% of the course] Lab [30% of the course]: lab reports…
Eng.Fouad
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Confidence interval for Uniform($\theta$, $\theta + a$)

I am encountering a difficulty with the following task. Have I made a mistake, or is this an inherent flaw in the notion of confidence intervals? (Other such flaws exist.) Consider a random sample $X_1,\ldots , X_n$ from a Uniform($\theta$,…
Stephen Herschkorn
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How do you "guess" a candidate for an UMVUE?

The following distribution is given $X \sim \operatorname{BIN}(1, p)$, then $\mathbb{E}(X)=p$ and $\mathbb{V} \operatorname{ar}(X)=p(1-p)$. The CRLB is computed with: $$ \begin{aligned} f(x ; p) &=p^x(1-p)^{1-x} \\ \ln f(x ; p) &=x \ln p+(1-x) \ln…
Tim
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standard error of sample mean

I am asked to calculate the standard error of the sample mean using bootstrapping for this data set y = c(4.9, 3.3, 2.2, 2.3, 1.6, 2.4, 4.7, 1.4, 1.7, 5.1) The solutions are as follows: set.seed(12345) nsim = 10^6 ybar.sim = numeric(nsim) for…
blueonken2
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Chi-squared Test for the Variance

An example of Chi-squared Test for the Variance on NIST website (https://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm) goes as follows: The observed variance for the 100 measurements of gear diameter is 0.00003969 (the standard…
techie11
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