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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What would you call an equation that determines the maximum value of a regression line on a bell-shaped scatterplot?

Please forgive the vagueness of my question, it has been a while since I have done this sort of math and I'm simply looking for the correct type of wording to further research this problem. Given that I have a data set that produces a scatter plot…
NickC
  • 121
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a best critical region of two parameters in normal distribution

This question is from Introduction to Mathematical Statistics written by Hogg et al In page 448, 1.6 Let $ X_1, X_2, \ldots, X_{10} $ is a random sample from a distribution that is $N(\theta_1, \theta_2)$. Find a best test of the simple hypothesis…
Minho Kang
  • 51
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Finding a PDF given a (strictly) right continuous CDF.

I have the CDF: $$ F(x)= \begin{cases} 0 & \text{if } x < 1 \\ \frac{x^2-2x+2}{2} & \text{if } 1 \le x < 2 \\ 1 & \text{if } x \ge 2 \end{cases} $$ I want to find the PDF and I noticed that $F$ is not continuous (at $x=1$), but it is right…
user78000
  • 269
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Maximum likelihood estimation and efficiency

Let $X_1, ..., X_n$ be independent observations of a random variable $X$ that has with probability $p$ the distribution $\mathcal{U}[0,a]$ and with probability $1-p$ the distrbiution $\mathcal{U}[0,b]$ where $a$ and $b$ are known with $a
Amarus
  • 1,697
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how to compute unbiased estimator

Suppose $X_1,X_2,...,X_n$ is a random sample of size n drawn from a Poisson pdf where $\lambda$ is an unknown parameter. Show that $\hat \lambda = \bar X$ is unbiased for $\lambda$. For what type of parameter, in general, will the sample mean…
notamathwiz
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Drawing Conclusions From Only Medians

At a small high school, the 12th grade is only 20 students. They all take the same five classes (English, Math, Science, History, and Latin) together. At the end of the year each student is assigned a numerical grade between 0 and 100 for each…
lawstudent02
  • 21
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Statistic question

1) A student took a chemistry exam where the exam scores were mound-shaped with a mean score of 90 and a standard deviation of 64. She also took a statistics exam where the scores were mound-shaped, the mean score was 70 and the standard deviation…
Andrew
  • 321
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Statistical tests of the form "is my PDF correct?"

Let's say we observe some data points $x_i$ and we hypothesize they come from some continuous r.v. X which has PDF $f$. I know that e.g. the Kolmogorov-Smirnov test can be applied to this kind of problems. Do these tests/problems of the form "is my…
peter.petrov
  • 12,568
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rms signal given covariance matrix

Hi I have a fairly simple question Say I have a covariance matrix C that describes the noise in some data series D, including correlations between different data points (so just a general correlated gaussian). I thought that if i wanted to work out…
Jim Wolson
  • 21
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prove that it is a pivotal quantity

My problem is that I have the distribution $f_{z}(x)=\dfrac{2z^2}{x^3}$, $0
Gabrielle
  • 21
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How can I prove the variance of residuals in simple linear regression?

How can I prove the variance of residuals in simple linear regression? Please help me. $ \operatorname{var}(r_i)=\sigma^2\left[1-\frac{1}{n}-\dfrac{(x_i-\bar{x})^2}{\sum_{l=1}^{n}(x_l-\bar{x})}\right]$ I tried.. using…
Guido Di Pietro
  • 407
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Transforming sum of random variables and conditional expectation

Homework warning I've been having a lot of trouble with questions where we transform a random variable with a sum of other random variables. I'll give an example and what I've tried to do (this is not an actual question from my homework but is…
astroturfdurf
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T'wo level full factorial design question

I need to prove the following identities for a factorial design experiment of the form $2^k$. $\overline{Y}(AB+)-\overline{Y}(AB-)=0.5$[$A(B+)-A(B-)$] $A(B+)=A+AB$ $A(B-)=A-AB$ $A=\frac{[A(B+)+A(B-)]}{2}$ ($\overline{Y}(AB+)$ is the mean of all…
Manko
  • 145
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Let $X_1, \dots, X_n$ i.i.d. from the $DE(\theta,b)$ Prove the MLE is asymptotically efficient

Let $X_1, \dots, X_n$ be i.i.d. from the $DE(\theta,b)$ distribution (DE is the double exponential). (a) Show that the MLE $\theta$ is the sample median. (b) Prove that the MLE $\theta$ is asymptotically efficient. For part (a): $$L(\theta) =…
anonyx2
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