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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Unbiased family of estimators and variance.

Given $X_1, \dots, X_n$ simple random sample with distribution $F_X$ -unknown-, i have to estimate $\mu = \mathrm{E}(X)$. Now, given the famility of estimators $\tilde{T} = \bigg\{\displaystyle\sum_{i=1}^n \alpha_iX_i : \ \displaystyle\sum_{i=1}^n…
balaya
  • 51
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Clarifying the rule: "R-squared is invalid for nonlinear regression"

I'm a novice trying to determine if the use of R-squared is valid for developing an exponential regression (of the form $y=a+b\,e^{cx}$ ). I've come across several articles online that say R-squared is invalid for nonlinear regression. That claim…
User1974
  • 425
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Why mean is the balancing point?

4,5,7,12,34 are the data points. Median is 7. But, why mean would be the balancing point here? I know the mean distribute the data points evenly among individuals, which means if any individual would’ve scored any point, he’d have scored the mean .…
Vinay Sharma
  • 79
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Can someone help me with this statistic question?

A firm decided to have a sales event that they take name cards from 1000 of their customers, and randomly distribute the cards back to those customers. And the customers who receive their own card will get 50% sales for all of the firms products.…
David Park
  • 63
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Find the density function of $Y=e^Z$ where $Z \sim N(\mu, \sigma^2)$

Find the density function of $Y=e^Z$ ,where $Z \sim N(\mu, \sigma^2)$ This is called the lognormal density , Since $\log Y$ is normally distributed.
izako5
  • 57
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Constructing an LR test for a concrete example and find its critical areas and power function

I am working on the following exercise: We are given an observation of a discrete RV $X$ with PMF $f(x \mid \theta)$ and $\theta \in \{0,1,2\}$ as in the table below. Find the LR test for the hypothesis $H_0: \theta = 0$ and list all possible…
3nondatur
  • 4,178
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Proving that this is a method of moments estimator for $Var(X)$ for $X\sim Geo(p)$.

Let $X\sim Geo(p)$ be a random variable, and $X_1,...,X_n$ a random random sample from the distribution of $X.$ Prove that $\frac{1}{2n}\sum^n_{i=1}X_i^2-\frac{1}{2}\bar X$ is an estimator in the methods of moments for $Var(X)$. Basically what…
Pwaol
  • 2,113
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Need help with Pearson criterion (chi-square) to check if the distribution is uniform

Let's assume we have X - a random variable, and its values are 1, 2, and 3. We also have frequencies for each of the values, which equal to 51, 40, and 65 respectively. So, this will look like this: X 1 2 3 n 51 40 65 And the question is…
Артем Макаров
  • 23
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hypothesis testing problem

I'm stuck at the following problem We have people picking one of A,B,C. According to a theoretical model people pick in the ratio $p^2:2p(1-p):(1-p)^2$ respectively. From a sample we have 42,52,22. Is the model correct? I know that I have to use…
Sdfasvg Asfgavf
  • 53
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What is a reasonable bound for integrating the standard normal distribution with a single tail?

This is a question I'm trying to figure out how to solve because my calculator does not allow me to evaluate improper integrals. I am trying to find the z that produces a small enough p to be negligible. In general I think I will need about 5 digits…
O.S.
  • 592
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You have 4 prizes, 3 tickets, n tickets- what is the probability of winning

You have bought 3 tickets in a lottery. There are n total tickets and 4 prizes. What are the odds of winning at least one prize? I thought of it like this: The total possible ways of extracting 4 prizes is: a= $${n\choose 4}$$ The possibilities of…
Ryan
  • 309
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Is $E(xy) \geq E(x) E(y)$?

Is $E(xy) \geq E(x) E(y)$ always? Where $E$ means expectation. Intuitively I feel like covariance should always be nonnegative, but I cannot prove why. Thanks for your help
badatmath
  • 4,065
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Find hazard rate of $X$ from its residual lifetime survival function

Given a random variable $X$ with survival function $S_X(x)$, I know that I can find the survival function of the residual lifetime rv $T_t=X-t|X>t$ by $S_{T_t}(x)=\frac{S_X(t+x)}{S_X(t)}$. But can I go the other way around, and find the survival…
Dillon Don
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Expectation of random variable with two vectors

I am reading this paper "Continuous Diffusion Analysis" and in page 7 there are a next formula $\mathbb{E}_{x,y}[d_S(x,y)]=\dfrac{1}{4}\sum_{i=0}^{n-1}\int^{1}_{-1}\int^{1}_{-1}|sgn(x_i)-sgn(y_i)|dx_idy_i$. I am trying to obtain this formula using…
juaninf
  • 1,264
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What is the minimum number of tests to achieve statistical significance?

I'm dealing with a situation where in a large manufacturing facility we have approximately $2000$ plumbing fittings of the same make and model. $3$ of those fitting have failed within the last year. Each causing major property damage. We suspect…
ziptron
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