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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Expectation of square of random variable and their mean.

The following easy proof is well known to all students of statistics. I studied it three years ago and at present I can not remember two steps of it. If you can help me a little. $$E({X_i}^2) = \mu^2 + \sigma^2$$ $$E(\bar{X}^2) = \mu^2 +…
Supriyo
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In a MOBA, is it possible for every character to have a <50% winrate?

In a recent discussion with friends we were discussing win-rates in a video game. One person suggested it made sense that every champion could have a less than 50% win rate, while another suggested this was impossible because every loss suffered for…
BenHaef
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Is pi lying on the ground, and on TV? - and on the sun?

Consider the leaves from a bunch of trees in a terraced plaza in the Autumn. It may well happen that the tiles of the terrace are squares whose length easily exceeds the length of the stem of the leaves (assuming leaves all of the same kind). Cannot…
Mike Jones
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99th Percentile: top 1% or top 2%?

If one achieves a score in the 99th percentile on an exam, is that score considered in the top 1% or 2%? How is percentile defined in statistics? I read this somewhere: It’s top 2% - being in the x percentile doesn’t imply top (100-x) percent…
user27343
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pairwise correlation of three random variables

Assume three random variables have all equal pairwise correlation. What are the possible values of this correlation? Can all of these values be achieved? The solution says $\rho \in [-\frac 12,1]$, but without any explanation. Can someone give me a…
John Peter
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How do I find the bias of an estimator?

My notes say $$B(\hat\theta) = E(\hat\theta) - \theta $$ And I understand that the bias is the difference between a parameter and the expectation of its estimator. What I don't understand is how to calulate the bias given only an estimator? My…
H4-math
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fair die or not, from 3D printer

I made a 3D printed die today, but depending on the heat applied, it may or may not be a "fair" die (i.e. have an equal chance of landing on each face). I have just tried rolling it 150 times. The frequency results came out to: $$…
Eumel
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Hottest Days of The Year

Recently, there has been much talk in the media of it being the hottest day of the year so far. It has always seemed to me that there are likely many more of these in the northern hemisphere than the southern. In the northern hemisphere "the year"…
Dan
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Calculate the product of two Gaussian PDF's

I'm trying to understand the origin of the formulas for the $\mu$ and the $\sigma^2$ from this side (stanford): https://ccrma.stanford.edu/~jos/sasp/Product_Two_Gaussian_PDFs.html As I have understood actually the product of two Gaussian PDF's is…
heiko
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Exponential distribution unbiased estimator

Let $$X_1, \ldots, X_n \overset{iid}{\sim} Exp(\lambda), \quad \lambda > 0$$ The Maximum-Likelihood-Estimator is given by $$\widehat{\lambda} = \frac{1}{\frac{1}{n}\sum_{i=1}^{n}{X_i}} = \frac{n}{\sum_{i=1}^{n}{X_i}}$$ and it's not unbiased: Using…
georgmierau
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Consecutive Coin Toss with static tosses

I'm writing an algorithm for a coin toss problem. But I have a problem understanding the calculation given. Here is the question: You have an unbiased coin which you want to keep tossing until you get N consecutive heads. You've tossed the coin M…
Shawn Mclean
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Calculate p value

taking stat 101, I was wondering how I could figure out the p-value, with the hypothesis mean being equal to -4 given the data below. Could someone explain the p-value?
Mark
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Precise mathematical translation of the 68–95–99.7 rule?(Not a proof!)

The rule: In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within 3 standard deviations of the mean in a normal distribution. About 68.27% of the values lie within 1 standard…
shooting-squirrel
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Where did this statistics formula come from: $E[X^2] = \mu^2 + \sigma^2$

I am studying statistics and I need some guidance as to where this formula came from. All I know is that $\displaystyle E[X^2] = x^2 \sum_{i=0}^n p_{i}(x)$
Person
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What is the T-distribution, and what is it used for?

(I'll post my own answer to this, but don't hesitate to post your own!) Student's t-distribution, or T-distribution, was introduced in 1908 by William Sealey Gossett writing under the pseudonym "Student". What is it, and what is it for?
Michael Hardy
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