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.

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Chances of getting mono from beer pong?

In a friendly game of Beer pong there is 1 cup that has been previously used by a person with mono. Assuming the cup is infected what are the chances that you drink the infected cup if you drink 4 cups out of the 10 in the cups triangle? In beer…
John
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How does the Kurtosis test for normality work?

For example, the skewness test statistic is based on averaging the x^3 of the data. If the distribution is symmetric, there will be similar number of positive x’s and negative x’s, thus x^3 and (-x)^3 roughly cancel each other with a small overall…
Richie Lee
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Consistency of sample variance $S^2$

Let $Y_1...Y_n$ be independent $N(\mu,\sigma^2)$ R.V.s. Their sample variance is: $$ S^2=\sum_{i=1}^n \frac{(Y_i- \overline Y)^2}{(n-1)} $$ Treating $S^2$ as an estimator, is the estimator consistent? Here is how I would do the problem and guidance…
nicefella
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Finding MLE from CDF

So I have the following $CDF$ and I was wondering how will I be able to get the Maximum Likelihood Estimator since we do not have the $PDF$ to work with. The following $CDF$ is an exponential distribution that is "shifted" if you will by $L$ units…
LearningIsPower
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Maximum Likelihood Estimation

I am stuck on this problem and help would be greatly appreciated! I have the following PMF (a modified Poisson Distribution). \begin{align*} \frac{\lambda^x e^{-\lambda}}{x!(1 - e^{-\lambda})} \end{align*} for some $\lambda >0$ and $x=1,2,3...$ I am…
nicefella
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Finding variance for RV=RV1(1-RV2-RV3-...)

When a AR model is fit using the R arima package, you get back the estimate and S.E. for all the coefficients and the "intercept". However, for a non-zero-mean process, the true intercept is really $\phi_0=\mu(1-\phi_1-\phi_2-...)$ where $\mu$ is…
Shaun Bharrat
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Delta Method and Expected Value

I would just like to check something regarding the delta method. After using the delta method to verify that, $$ \sqrt(n)(g(X_n)-g(\mu)) \sim n(0,\sigma^2 [g\prime(\mu)]^2) $$ we cannot generally assume that assume that $E(g(X_n))=g(\mu)$, right?…
user191919
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Rao-Cramer lower bound

Find the Rao-Cramer lower bound if the random sample $X_1,X_2,...,X_n$ is taken from the distribution with the p.d.f. $$f(x;\theta)=\frac{1}{\theta}x^{\frac{1-\theta}{\theta}}$$ where $0
Mike90
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Normal sample: alternative proof of $(n-1)S^2|\bar X \sim \chi^2(n-1)$

Let $(X_1,X_2,..., X_n)$ be a random sample from a normal population with mean $0$ and variance $1$. I would like to show that $$(n-1)S^2|\bar X \sim \chi^2(n-1).$$ I know there is many way to do this, I would like to have your opinion on the…
user14108
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summation identity - statistics

What does this summation simplify to? $$ \sum_{x=0}^{y} \frac{1}{x!(y-x)!} $$ I tried applying common formulas (Maclaurin series, binomial coefficients, etc. but nothing seems to match up to it). Any tips would be appreciated. Thanks.
icobes
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Poisson distribution

Assume the number of episodes per year of a disease follow Poisson distribution with parameter $u=1.6$ per year. 1) What is the probability that two siblings will both have three or more episodes of disease in the first two years of life? ans:…
noob
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Variance of difference of two sample means from the same population

We take two samples from $Z$ of size $n_1$ and $n_2$ and take the difference of the mean of these samples. Both should have the same expected value, so the mean is zero. But what is the variance of this difference?
snoram
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moment generating function of a pmf

A pmf is shown below along with its mgf. I was wondering how I would calculate moments for the marginal distributions. Would I let t1 = 0 to find the marginal distribution of y? Would I then differentiate that expression and evaluate it at 0 to find…
icobes
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How do I get a rate per hour that can be negative into a positive score for ranking purposes?

I am writing a report that allows my employer to rank employees by productivity and fault rate. Employee ranks are based on productivity (value of 25%), supervisor input(value of 25%) and fault rate(50%). Catching a fault awards you a single point,…
davidahines
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Statistics: If $X_1$ and $X_2$ are both normally distributed then explain why $X_1 - X_2$ can be standardized with mean 0 and standard deviation of 1

I am currently studying hypothesis testing for two populations and I would like a math major or someone experienced to explain to me why this particular statistic has a mean of 0 and a standard deviation of 1: $$ z_{\bar{X_1}-\bar{X_2}} =…
poli-sci
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