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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uncertainty of slope.

i have a graph that i fitted a line on it using least squares fit. Now i want to calculate the uncertainty of slope. i calculated the standard error of slope and now i have this question: the uncertainty of slope is "slope ± standard error" or it is…
afagh
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One tailed or two tailed

Ok so this the question: An administrator at a medium-sized hospital tells the board of directors that, among patients received at the Emergency room and eventually admitted to a ward, the average length of time between arriving at Emergency and…
Need help
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Kolmogorov-Smirnov test

Five observations from an underlying loss distribution are: $0.1,\ 0.2,\ 0.5,\ 0.7,\ 1.3$. Find the value of the Kolmogorov-Smirnov test statistic for test that the underlying distribution has p.d.f. $f(x) = 4/(1+x)^5$.
nong
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General probability equation

I am really struggling with statistics. I am trying to come up with the basic equation/concept of calculating the probability for something. for example: I know that the probability of coming up with exactly 3 heads in 4 flips of a coin is 1/4,…
Lydia
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Invariance of MLE

Random sample has pdf:$f(x|\theta)$ Then the MLE of $\theta$ is $$\hat{\theta}=\arg\max_{ \theta}\sum_{i=1}^n\log f(x_i|\theta)$$ $\tau=g(\theta)$ My question is why $\tau$ 's MLE is $$\hat{\tau}=\arg \max_\tau\left[\max_{\theta\in…
Lookout
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What does SSB and SSW of ANOVA tell you about your data?

This might be a stupid question. I know how to calculate them but mine not sure what they are telling me about my data set. What does it mean if $\sum $$(SSB)^2$ $\ge \sum (SSW)^2$, or vise versa, or does $SSB$ and $SSW$ only have meaning when you…
toom
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What is the distribution of the euclidean distance between two normally distributed random variables with non-zero means?

Assuming two uncorrelated random variable (RVs) with Gaussian distributions $x\sim N(m_1,s)$ and $y\sim N(m_2,s)$, so with non-zero mean and same variance, what is the distribution of $z=\sqrt{(x^2 + y^2)}$? Is there a known parametric distribution…
Ana Maria Popescu
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Let $X_1,\ldots,X_n$ i.i.d. negative binomial. Find the best unbiased estimator for $P(X\le3)$

I am not sure where I should even start with this problems. I know that the sum of negative binomial random variables is itself a negative binomial random variable. I am sure that I can show that the sum is also a sufficient and complete statistic.…
mathestats
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Degree of freedom

I have learnt from solving different statistical problems that if we have a sample of size $n$ picked from the population with normal distribution, the degree of freedom for, say, Student distribution or Chi-square distribution distribution will be…
user1812
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Statistical Methods: Analysis of Normal Measurements

Show that, if $\sigma$ is unknown, the likelihood ratio statistic for testing a value of $\alpha$ is given by $$D = n \log\left(1 + \frac{1}{n-1}T^2\right)\;,$$ where $$T = \frac{\hat{α} -\alpha}{\sqrt{s^2/n}}$$ So far, I have the…
Mauricio
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Need help interpreting weird result for seemingly simple problem.

I am solving a problem and just can't wrap my had around the result I'm getting... Here it is: So my next step would be setting derivative equal to zero and solving for Theta... Are my calculations wrong?... I would appreciate any constructive…
user175755
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Variance of first 30 odd numbers

How to calculate variance of first 30 odd numbers ? The method I used requires finding the mean and subtracting each number with it and then squaring the result . Its getting difficult . I used this : Any other way to calculate ?
Micheal
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Proving the PDF of the $r$th order statistic

If $X_1,...,X_n$ are iid random variables with $r$th order statistic $X_{(r)}$ I'm trying to prove it's pdf is $$f_{(r)}(x)=\frac{n!}{(r-1)!(n-r)!}F(x)^{r-1}[1-F(x)]^{n-r}f(x)$$ Is is true for $r=1$. I then assume true for $r$. The only step in this…
Freeman
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Calculating $\mathrm{Var} (Z|Z|)$

Suppose $Z\sim N(0,1). $ How can I calculate $\mathrm{Var} (Z|Z|)$? I know $\mathrm{Var} (Z|Z|)= \mathrm{E}(Z^4)-\mathrm{E}^2(Z|Z|)$
nssanji
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permutation test for one-way ANOVA?

I want to know what steps to do the permutation test (and the R/SAS code) for one-way ANOVA? Would you give me the specific steps? Thanks, Buddies!
Rex Woo
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