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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Statistics - Confidence Interval for a Population Proportion Formula

I am having a conceptual hard time understanding where this formula came from. It does not seem to make any sense to me. Could someone shed some light on this: "The natural estimator p is $\hat p = \frac{X}{n}$, the same fraction of success. Since…
Low Scores
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Calculating cumulant from data set

Given a data set $x = \{ x(n) \mid n=1,\ldots,m\}$ how do I calculate the $p^{th}$-order cumulant? In particular I need to calculate the 4th-order cumulant. I found that I can calculate the cumulant from moments, but I also don't know how to…
Techy
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Expected value of geometric distribution

I watched $\text{Statistics} \space 110$ from Harvard University through YouTube. From lecture 9, the expected value of the geometric distribution is: $$\sum\limits_{k=0}^{\infty}…
sunmi yoon
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Not complete but minimal sufficient statistic

Let $X =(X_1,\ldots, X_n), ~ X_i \mathrm{iid} \sim \mathcal N ( \theta, \theta^2), ~ \theta \in \Theta = \mathbb R \setminus \{0\}, ~ T(X)=(\sum_{i=1}^n X_i, \sum_{i=1}^n X_i^2)$. I figured out that $T(X)$ is sufficient. To show that it's not…
xxx
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Find the Bayes estimate of $θ$

Can someone help me solve this out, please? Thanks a lot. Find the Bayes estimate of $\theta$ based on a single observation of $5$ from a distribution that is uniform on the interval 0 to $\theta$. Use square-error loss and a prior distribution of…
nong
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Finding the covariance

Can you help me find the covariance of $\mathrm{Cov}(5X+3Y, 7X-Y)$ I've been looking up formulas all day and I can not find on that adds both x and y just constants. Thank you! $Mx=2, My=7, \mathrm{Var}X=4, \mathrm{Var} Y=9$, and…
Leah
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How to interpret p-value in this problem.

The following is the question in particular, I got this question wrong. However nothing I run across explains why it is wrong. I answered C because with a p-value of 0.087 we don't have an "unusual" enough outcome to reject the null though the…
DanBaba
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How do I determine if my variance is significant?

For a given group of data, I have both a mean and variance (already calculated). Looking over the raw spread of data, and its numerous outliers, I expect that variance will be high. My question is -- now that I have my variance calculated, what do I…
Raven Dreamer
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Formal definition of maximum likelihood estimation

We typically introduce maximum likelihood by considering a family of distributions $\{P_\theta: \theta \in \Theta\}$ which admit densities $f_\theta$ with respect to some underlying measure $\lambda$. We observe a random vector $X \sim P_{\theta_0}$…
guy
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Does the empirical CDF converge in $L^1$ and $L^2$?

I am somewhat confused with the empirical distribution function: Assume we have $X_1, X_2, ...$ iid real-valued random variables with true distribution $F_0$. Then by the Theorem of Glivenko-Cantelli, $$| \hat F_n - F_0 |_\infty \longrightarrow…
Emil
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when can I say there is a relationship between events?

I am by no means a math expert, but I am analyzing very large weather data data for a computer science course .I am taking away all the weather related issues out of the analyzing and just looking strictly at it in the eyes of statistics. Lets say…
user2924127
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How close are these events?

I'm a computer programmer and we're running into a weird error on our website. We have a large number users who do a certain task. Between the entire set of users, this task happens about once every 20 seconds, but of course each user is…
Aric TenEyck
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Why is $\sqrt{n}/n$ a acceptable proportion of outliers?

Recently I found a paper which stated that $\sqrt{n}/n$ is the maximal acceptable proportion of outliers for n given data points. Unfortunately they only quote a book, which is quite out of my price…
betlor5
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What distribution would describe this?

I start with 100 eggs, 10 of them being broken. I randomly select eggs without replacement until they are all split into baskets of 10 eggs each. Here's what I know: Best case scenario all 10 bad eggs go into 1 basket, giving me 9 good baskets out…
gregsan
  • 131
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Ranking system that factors in both positioning and clustering?

I'm not sure how to express my problem in proper semantic terms, so please forgive me if I am unclear, waffling or use the wrong terminology anywhere here! I'm trying to find a ranking system that will not only take into account the relative…
Shaul Behr
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