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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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Bounding the variance of an unbiased estimator for a uniform-distribution parameter

$X_1,\ldots,X_6$ is a sample from a uniform distribution $ \left[ 0, \theta \right] $, $\theta$ is $[1,2]$. Find an unbiased estimator for $\theta$ with variance less than $\dfrac{1}{10}$. I thought the M.L.E is $\max \left( X_i \right) $,and the…
nina li
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How can I estimate the centre of mass with obscured/missing data?

How can I estimate the centre of mass for a sample of simple point objects with uniform mass distributed in 2 dimensions when parts of the sample are obscured? For example consider a collection of points where we have absolute knowledge over most of…
AnnanFay
  • 490
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How to calculate probability distribution for combination of functions

please excuse (or change, if possible) the title if it doesn't make sense. I have a problem which is something like this: You have a variable $i$ which starts at $i=1$. You also have a target number of $j$, and you have an n-sided die (in my case…
allouis
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Can I use ANOVA when I have negative values in my data?

I was trying to analyze a data with negative values. Is it possible to use ANOVA in this case?
leian
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Finding a pivotal function from uniform distribution

Let $X_1,...,X_n$ be a random sample from a uniform distribution $(0,\theta)$. I have found the maximum likelihood estimator to be $Y_n = \text{max}\{X_1,...,X_n\}$ The solution then claims that $\frac{Y_n}{\theta}$ is a pivot. I don't understand…
mrnovice
  • 5,773
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Normal distribution Questioning

The weights of a group of children are approximately normally distributed with mean 15kg and standard deviation=1.75 kg What proportion of the children will weigh 13 of or more? Can someone help me solve it?
AYESHA
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Metric for calculating lopsided distributions

I have a list of ~20 numbers: 1200, 1200, 360, 360, 300, 250, 180, 180, 180, 180, 180, 90, 90, 90, 90, 45, 10, 0, 0 I am looking for a metric that determines the lopsidedness (maybe skewness) of this distribution. For the above example, I would…
beta
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Statistics: Hypothesis Testing

Hypothesis Testing I have 4 groups of data for four different locations i.e. A, B, C and D (close to each other). In each group, there are 3 columns of data (x, y, z) showing the temperature at the location taken by thermometer at a different height…
Student45z
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Which statistical test should I use in this situation (sample size question)?

Assume I have 5 millions oranges. Now I want to test a hypothesis. If there is a black dot on an orange, then the orange is BAD. Within these 5 millions oranges, I have been told that which are bad. However, I cannot check all bad oranges to see…
Giordano Fearghas
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Is there an ideal $k$ such that the sequence $\mathrm{frac}(kn)$ is most evenly distributed?

I am generating a sequence of numbers in $[0..1)$ where the $n$th number in the sequence is $f(n)=\mathrm{frac}(kn)$ for some constant $k$ and $\mathrm{frac}(x)=x-\mathrm{floor}(x)$. I want numbers in this sequence to be distributed as evenly as…
spraff
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Statistical Data Reconstruction

As I read an introductory statistics book, a question struck me which am curious to find a good answer for. Background The author teaches that statistical classification (understand this to mean organizing raw data into say classes -e.g by grouping…
JWL
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Statistics - Chebyshev's rule, my answer is wrong for some reason?

I have the following problem : Determine what age interval will contain at least 95% of the data (Chebyshev's) ? Now, I have standard deviation of 1.516, mean of 19.211. The formula is $1-(1/k^2) = .95$ So I solve for k to get $\sqrt 2$. Now, I…
FabolousPotato
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How does Law of Total Probability apply here?

Cumulative Distribution Function for Sum of Continuous Distributions That means $X\in x$ is a partition of $X+Y$? But how could that be? It only accounts for the $X$ part.
A_for_ Abacus
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Probability Density Function for Gamma Distributions

Shouldn't probability density functions be in the form of $$P(X\in dx) = \cdots$$ Why does the one for gamma distributions divide by $dt$? $T_r =$ time of $r^\text{th}$ arrival after time $0$ in a poisson arrival process with rate $\lambda$. And…
A_for_ Abacus
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When to Use Normal Approximation?

Do we use normal approximation when discrete distributions are hard to solve? For example, $P(X\ge 7000)$ where is $X\sim\operatorname{Binomial}(13000, 0.7)$. Obviously, summing each case manually cannot be done and the summation is difficult to…
A_for_ Abacus
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