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
2
votes
2 answers

Confidence interval in statistics

I really need help on this question. I am taking an introductory statistics class, and here is the question: A taxi company wants to determine if customers will accept self driving cars. The company authorized a survey and subjects were to be…
user6873843
  • 71
2
votes
2 answers

Boxplot Skewness

I do know there are some rules about boxes and whiskers to determine the skewness in a boxplot, but I am confused with some rules in this particular case: Keeping in mind the rules, in this boxplot the median falls to the right of the center of the…
Christian Andrews
  • 83
2
votes
1 answer

Sufficient statistics

I'm learning about sufficient statistics and I understand basic stuff that it is the minimum information we need to represent a statistic (very vague definition, I know. I'm learning). I'm trying to solve problems in that. The problem is suppose a…
0x0
  • 2,641
2
votes
1 answer

Calculate Confidence Interval With 20 Samples

I have 20 samples of network latencies. Each sample consists of 5000 numbers (in milliseconds). I would like to find a 95% confidence interval for average (Mean), 90th percentile, 95th percentile and 99th percentile for network latencies. I have…
Ibrahim EL-Sanosi
  • 21
2
votes
1 answer

"Outlier" vs "Potential Outlier"

Is an outlier, defined by being further than 1.5x the range of the Interquartile Range outside of the IQR, an actual outlier or merely a potential outlier? Different sources seem to use different semantics.
Tahsis Claus
  • 123
2
votes
2 answers

Gamma distribution and pdf

Let $X \sim \mathsf{Gamma}(2,3)$ and $Y = 2X.$ Find the pdf of $Y$ at $y=13.5.$ Attempt: $f_X(x)= 2*[1/9*\Gamma(2)]*x*e^{-x/3}.$ Do I have to integrate now?
user417179
  • 39
2
votes
2 answers

Formulae for combining statistical moments

I am writing code to calculate statistical moments (mean, variance, skewness, kurtosis) for large samples of data and have the requirement of needing to be able to calculate moments for subsections of the sample (in parallel), then combine/merge…
Simon Cowen
  • 123
2
votes
1 answer

Question about variance and its relation to standard deviation

I understand from my lecturer that variance an standard deviation are central to statistics. I do not understand the signifigance of both values, except that both measures the variability, and variance is the square of standard deviation. Why is…
Yellow Skies
  • 1,710
2
votes
1 answer

How do I show that this is a T distribution?

$Y_1,...,Y_n$ is a random sample from a $N(\theta,\theta)$ How do I show that $$\frac{\sqrt{n}(\bar{Y}-\theta)}{s}$$ is a t-distribution with n-1 degrees of freedom? By the way, $$s^2=\frac{\sum_{i=1}^n(Y_i-\bar{Y})^2}{n-1}$$
sucksatmath
  • 877
2
votes
1 answer

Hypothesis Testing for uniform distribution

Let $X_i; i=1,2,3,\dots,n$ be iid samples from the uniform $U(0, θ)$ distribution, with $θ$ being the unknown parameter of interest. Consider the testing problem $H_0 : θ = θ_0$ versus $H_1 : θ > θ_0.$ One possible test is to reject $H_0$ when…
joe
  • 301
2
votes
3 answers

How is it that the required sample size for a specified error and confidence is not dependent on population size?

When calculating confidence intervals for population parameters, the population size is never a factor, rather sample size and the estimated parameter are used. It seems to me very counter-intuitive that to assert with a certain confidence that a…
jsj
  • 535
2
votes
0 answers

Benford's Law Application

Benford's law is a simple empirical tested first digit distribution in data series. I do my Macroeconomics Thesis and I am going to propose to evaluate various filtering processes. I have found an IMF article where they use the first digit law to…
Commissar Vasili Karlovic
  • 207
2
votes
1 answer

Show E$\big[\frac{\bar{X}(1-\bar{X})}{n}\big] = \frac{(n-1)p((1-p)}{n^2}$

I am trying to show E$\big[\frac{\bar{X}(1-\bar{X})}{n}\big] = \frac{(n-1)p((1-p)}{n^2}$, for $X_1, X_2,\ldots, X_n\sim\operatorname{b}(1,p)$. I can get to E$\big[\frac{\bar{X}(1-\bar{X})}{n}\big]$ = $\frac{1}{n^2}(np) -…
BenL126
  • 23
  • 3
2
votes
2 answers

Minimize Expected squared Prediction Error (EPE)

I have difficulty understanding when minimizing expected squared prediction error: $$\operatorname{EPE}(\beta)=\int (y-x^T \beta)^2 \Pr(dx, dy),$$ how to reach the solution that $$\operatorname{E}[yx]-\operatorname{E}[xx^{T}\beta]=0.$$ From A…
Jiang Xiang
  • 257
  • 1
  • 2
  • 12
2
votes
1 answer

Determining sample size

I have a large set of data and a copy of that data. The whole data set is $n$ bytes. I want to be 99.999% certain that the sets are identical. Assuming that copying errors occur randomly, how many bytes do I need to randomly select and compare…
Clara Höfner
  • 331
1 2 3
…
99 100