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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Probability of no students being mechanical engineers

In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major. Suppose five students from the class are…
Question_Guy
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What Percentile Do I fall in with this test score vs average?

I just took an online test and I was notified that the average score for the test was 45% (out of 100%) and I received a 72%. Using these 2 pieces of information would it be possible to calculate under what percentile I fall for test scores?
Juan Velez
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Integration limits and probability density

So I've got the density function for the $2$-dimensional random variable $(X,Y)$: $$p(x,y) = \frac{4}{3}xe^{-x-y} $$ when $ 0 < y < x$. Otherwise, it's $0$. I am now interested in the density of the random variable $W = X + Y$. This is given…
Stan fesn
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Formula to generate a grade

I hope this question is appropriate for this site, if not sorry in advanced. I'm trying to come up with a formula to generate a grade, which will take into consideration the diffculty level of the questions. The person taking this quiz can determine…
Udi Idan
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Rao-Blackwell Theorem - Best estimator (Statistics)

Let $X_1 , ... , X_n$ be a series of independent random variables following a Bernoulli distribution with parameter $\theta$. And let $S_n = \sum_1^n X_i$. We know an unbiased estimator of the variance for the Bernoulli distribution: $$1/2 * (X_1 -…
clds
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Using Basu's Theorem

I have the following question: What have I done so far: I have showed that Y4 is sufficient and complete for theta. Now I need to apply Basu's theorem, and I am not exactly sure how to show that Y1 / Y4 or (Y1+Y2)/(Y3+Y4) are ancillary statistics.…
icobes
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Probability of Big Leads in CoinTossing Game Evaporating

In a Coin Tossing game, how is the probability of a lead change affected by the size of the lead that one side has - taking into account the number of coin flips remaining in the game? I have asked for help at Statcrunch.com, Hyperstats.com and…
Pseudoego
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Grading system with multiple judges

This is a practical question, I'm not sure if it's on-topic here. So sorry if it's not. There is a competition where judges decide the score competitors by summing their performance mark in several aspects, and different competitors might be graded…
arax
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Probability of getting a parking ticket

The city of Ithaca, New York, allows for two-hour parking in all downtown spaces. Methodical parking officials patrol the downtown area, passing the same point every two hours. When an official encounters a car, he marks it with chalk. If the car is…
Max93
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Finding the distribution of $\frac{1}{\sigma^2}\Big( \sum_i^m (X_i-\bar{X})^2+\sum_j^m (Y_i-\bar{Y})^2 \Big)$ where $X_i$ is from a normal sample

Let $X_1,...,X_m$ and $Y_1,...,Y_n$ be independent random samples from normal distributions $N(\mu_1,\sigma^2)$, $N(\mu_2,\sigma^2)$ respectively, where all parameters are unknown. Let $$S^2=(m+n-2)^{-1}\Big( \sum_i^m (X_i-\bar{X})^2+\sum_j^m…
Freeman
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Showing family is NOT complete

How would I show that $$f(x;\theta) = \frac1{2\theta}$$ where $x$ is between positive and negative $\theta$ and $\theta$ is between $0$ and $\infty$ is NOT a complete family? I know that I need to find a non-zero function $u(x)$ whose expectation…
icobes
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do discrete probability distribution functions need a countable number of outcomes?

Everywhere I see on the internet they say that discrete probability distribution functions have a countable number of outcomes, and continuous have uncountable infinite number of outcomes. However if your domain is infinite dimensional with finite…
Matthew Liu
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Show that in this case $\rho \geq -\frac{1}{n-1}$

The bounds of correlation coefficient $\rho$ is shown to be $\pm 1$ in class. In many situations the bounds are sharper, i.e. they stay away from $+1$ or $-1$. Consider the random variables $X_1,\dots,X_n$ such that $E(X_i)=\mu$,…
Username Unknown
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confidence inteverval $95\%$

how do I go about finding the $95\%$ confidence interval when I have $n=12, s_x=0.66$ and $u=35.72$ and also how many more samples would I need to reduce the "length" of the interval by half? so I looked in the solution and it…
jgh123987
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Fill chart using final data

so all I know is that: n=100. i have 5 departments within the numbers: 0-1000. md = 500. avg =490. lower decile=200. upper quarter=600. I really don't know how to use the formulas of each if I don't have any data.(fx,Fx etc) notice: this chart is…
Noy Sapir
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