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
1
vote
1 answer

Probability distribution of $f_X(x) = \frac{1}{3}(\frac{2}{3})^x$

Suppose X has the geometric pmf $f_X(x) = \frac{1}{3}(\frac{2}{3})^x, x=0, 1, 2, ...$ Determine the probability distribution of $Y = \frac{X}{(X+1)}$. Note that here both X and Y are discrete random variables. To specify the probability distribution…
dollar bill
  • 265
1
vote
0 answers

Which distribution if repetitions in Metropolis Algorithm are neglected?

I'm a chemistry guy and in a program I wrote, I use a Metropolis acceptance criterion in order to determine whether my algorithm is allowed to go to a different part x' of the problem. This is done like this: 1. Generate x'. 2. With probability…
chemGuy
  • 11
1
vote
0 answers

Distance between points of different poisson point processes

I have two different 2D Homogeneous Poisson Point Processes $Λ_1$ and $Λ_2$ with densities $λ_1$ and $λ_2$. The PDF of the distance of the nearest point to the origin $(0,0)$ for each HPPP is known $f_{R_1}(r)=2πλ_1re^{(-λ_1πr^2)}$,…
billy
  • 23
1
vote
1 answer

How to find covariance of vectors?

Given $X=(X_1,X_2,X_3)^T$ distributed as $N_3(\mu,\Sigma)$ with $\mu=(1,-1,2)$ and $\Sigma= \begin{pmatrix} 4&0&-1 \\ 0&5&0\\-1&0&2\\\end{pmatrix}$ Find whether $(X_1,X3)$ is independent of $X_2$ I know the definition of covariance is…
AColoredReptile
  • 2,729
1
vote
2 answers

One Way Anova Hypothesis Test

My professor asked this question Why is the hypothesis test correct $H_0: \mu_1=\mu_2=\mu_3$ $H_a:$ at least one different And these hypothesis wrong $H_0: \mu_1=\mu_2$ $H_0: \mu_2=\mu_3$, $H_0: \mu_1=\mu_3$ So basically why cant we say that…
user83157
  • 89
1
vote
0 answers

standard error of a correlation coefficient

I would like to establish the proof for the standard error of a correlation coefficient. Assume that we have two iid samples $\{X_i\}_{i=1}^N$ and $\{Y_i\}_{i=1}^N$ We know that the sample correlation is given by $$\text{SCor(X,Y)}=\frac{\sum_i…
7zf
  • 194
1
vote
2 answers

How to know which coin land on head the most given a data set?

Suppose I have 2 coins that I don't know what the probability of it landing on head is. It can be even (i.e. 50%) or it could be 2 biased coins that lands on heads most of the time. I do not have access to those coins but someone did some flipping…
jun
  • 113
1
vote
0 answers

construct an unbiased estimator for variance based on X1 and X2

I have a couple of questions: Suppose $X_{1},...X_{n} \stackrel{iid}{\sim} N(0,\sigma^2)$, where $\sigma^2$ $\in R^{+}$ is unknown. I need to find a sufficient statistic for $\sigma^2$, an unbiased estimator of $\sigma^2$ based on $X_{1}$ and based…
Ismael
  • 11
1
vote
1 answer

What is the principle due to which the QQ plots work and give a straight line if the sample data belongs to that distribution?

I understand that if I have a sample of data which follow Normal Distribution then if I plot the sample data's quantiles against the normal theoretical quantiles then I will observe that the points are closely following a straight line. But why are…
Kaustav Choubey
  • 11
1
vote
2 answers

Asymptotic variance of an estimator of the parameter of esponential distribution.

$**X**=\left(X_1,...X_n\right) $is a simple random sample from an exponential distribution $p\left(x;\theta\right)$, where $\theta$ is the parameter. $g_n\left(**X**\right)$ is an estimator of $\theta$. And…
user44618
  • 21
1
vote
1 answer

Required sample size for T-test and ANOVA

I remember that in using z-test vs t-test, the required sample size for z-test is n>30 while in t-test n<30 (Generally, is this the answer for the maximum sample size for t-test?) In ANOVA, I know that the groups must be at least two but I don't…
X's
  • 25
1
vote
1 answer

Is it possible to have $E(X)=0$?

We are given that the probability density function (PDF) of $X$ is $$f_X(x):=\begin{cases} cx^2& |x|\leq1\\ 0&\text{otherwise}\end{cases}.$$ Now, I find first the constant $c.$ What I got is $3/2$ (I don't know if this is correct.) Then I tried to…
X's
  • 25
1
vote
1 answer

How to construct a compact confidence region of $(\mu,\sigma)$ look for a normal distribution?

I am working on an exercise, where given $n$ iid observations $X_1,X_2,\ldots X_n\sim\mathcal{N}(\mu,\sigma^2)$, construct a compact $95\%$-confidence region $C \subseteq \mathbb{R} \times \mathbb{R}^+$ for the parameter $(\mu,\sigma)$. I did the…
3nondatur
  • 4,178
1
vote
1 answer

Fixing a statistical measure to analyse my data?

This is my first time posting here. So I am a Chemical Engineer working on quantifying the strength of my materials. Basically I synthesise beads and press the beads using a piston and see what load they are breaking.So for each sample I'll repeat…
wulf
  • 11
1
vote
2 answers

Singapore Math 6th grade probability problem

Karen has 12 cards, each written with a letter from the word PENNSYLVANIA. She picks a card at random. Without replacing she picks another card at random. Find the probability she picks two vowels. I was sure the answer is…
Gamliel Beyderman
  • 29
1 2 3
…
99 100