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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Derivation of Mode of grouped data

A formula to calculate the mode for grouped data's is given in my text book: Mode = $l + \dfrac{(f_1 - f_0)h}{2f_1 - f_0 - f_2} $ Where, $l = $ lower limit of the modal class, $h = $ size of the class interval, $f_1 = $ frequency of the modal…
BurntPi
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What is CDF - Cumulative distribution function?

Could someone please explain in layman's terms what CDF is? If someone could show a real-life example where this could be useful, it would be great.
Mark Zimmers
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Covariance of two random vectors

IF I have $X,Y_1,...,Y_n$ iid then how do I calculate: cov $\left [\begin{pmatrix}X\\.\\.\\.\\X \end{pmatrix}, \begin{pmatrix}Y_1\\.\\.\\.\\Y_n \end{pmatrix}\right]$?
usainlightning
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How to find mean and median from histogram

Solution for finding mean : The problem faced when i saw a video to evaluate the mean https://www.youtube.com/watch?v=vMrc6dP8pCo According to the video, the lecturer said that, we can take the average of the measurement intervals. so…
user52950
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For the binomial distribution, why does no unbiased estimator exist for $1/p$?

Suppose that $X \sim \mathrm{Binomial}(n,p)$ for $0 < p < 1$ Why does no unbiased estimator exist for $1/p$? My approach: We try to find the structure of $E_p(U(x))$, where $U(x)$ is any estimator of $1/p$. Now, we will…
user123276
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Help with proof of expected value of gamma distribution

I am struggling with this proof of the expected value for the gamma distribution. I need help with the step indicated by the red arrow. Could someone please break it down for me. Thanks.
YoungGrandpa
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How to get the standard deviation of a given histogram (image)

I have a doubt: How to get the standard deviation of a given histogram? I'm looking for it on the internet. But I got Nothing. For example the case of this image below Thanks in advance!
user157308
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Goldfish in a lake

It is known that many people dump their pet goldfish into lakes, when they want to get rid of them with no remorse! We wish to calculate the number of goldfish in a small lake, in which there are several other fish of various species. For this…
Juan Manuel Prada
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Example of Sufficient and Insufficient Statistic?

I am having trouble understanding the concept of a sufficient statistic. I have read What is a sufficient statistic? and Sufficient Statistic (Wikipedia) Can someone please give an example of: a simple (but non-trivial) statistical model a…
Andrew Tomazos
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Why "bother" with a null hypothesis at all?

(note: this is a very basic probability question, so it is highly probable (heh) that it is a duplicate) Every time I am trying to get into statistics (again), I am always lost at hypothesis testing. My basic question is - why do we form a null…
Karel Bílek
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How can you trust a bettor?

Two friends of mine are trying to convince me that they are good at betting. They infact have a certain profit after n bets. They provided me with all the bets they have made so far: odds, outcome and amount bet. How can I check if their wins are…
KingBOB
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What's the difference between MUTUALLY EXCLUSIVE and PAIRWISE DISJOINT?

When I study Statistical Theory, I find that these two concepts confuse me a lot. By definition, if we say two events are PAIRWISE DISJOINT, that means the intersection of these two event is empty set. If we say that two events are MUTUALLY…
J.Bao
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Definition of mean as an integral over the CDF

I'm reading a statistics textbook which defines the mean of a random variable $X$ with CDF $F$ as a statistical function $t(\centerdot)$, where $$ t(F) = \int x \, dF(x).$$ Can someone explain this definition? I'm familiar with the definition of the…
John
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Maximum likelihood and sufficient statistics

$$f_T(t;B,C) = \frac{\exp(-t/C)-\exp(-t/B)}{C-B}$$ where our mean is $C+B$ and $t>0$. so far i have found my log likelihood functions and differentiated them as follows: $$dl/dB = \sum[t\exp(t/C) / (B^2(\exp(t/c)-\exp(t/B)))] +n/(C-B) = 0$$ i have…
R.M
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Estimate the size of a set from which a sample has been equiprobably drawn?

Here is the problem I'm trying to solve: In order to send spam, a spammer generates fake nicknames, by picking random girl names (and appending a random number to it). I suppose it randomly and fairly picks names from a fixed list, and I get to…
b0fh
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