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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How to calculate an expected value from a cluster of results

I have a vector of points r where each element has an x and y value. For every one of those points there is a z value, which corresponds to a measurement taken at position r. If I have say n measurements taken at n different positions (for example…
Edd
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Question about the logic behind hypothesis testing

Let us say that we have this following problem: "A government agency claims that more than 50% of US tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 86 that were filed electronically. Test…
poli-sci
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Can I calculate a percentile given only quartile values?

It's been a while since I took a statistics course, but this question came to mind the other day. Let's suppose that I am looking at Salary data, but the only data provided is the quartiles. For example: Q1 = 25 percentile = 40 000 Q2 = 50…
NT3RP
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stats - calculate marginal pdf of $f(x,y)$ - limits of integration?

I have the following equation $$ f(x,y) = \frac{2}{x^2 (x-1) y^{(2 x-1)/(x-1)}} \quad \forall x>1, y>1 $$ I am trying to find that marginal pdf w.r.t. $x$, $f_X(x)$. Normally I would just take $\int f(x,y) dy$ using $x$'s domain as limits, aka over…
SheerSt
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What does the (1-alpha) mean in confidence interval?

same as title, what does it represents? I know alpha is the percentile we are trying to reach. such as if we are trying to get to 95% CI , then 0.05 would be 1-alpha . the question is :explain what is meant by the“1-ɑ”part of a confidence interval
user1919987
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Chi-square distribution

$X_1$ and $X_2$ are independent random variables. $X_1$ and $Y = X_1 + X_2$ have $\chi^2$ distributions with $r_1$ and $r$ degrees of freedom and $r_1 < r$. How would I show that $X_2$ has a $\chi^2$ distribution with $r - r_1$ degrees of freedom?
icobes
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How would I calculate the better performance based on percentages?

I've been looking at how the characteristics of web content relate to the number of views it receives. I looked at the percentage of content with that characteristic, and then the percentage of views on that content. For example - 16% of pages are…
John
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Testing if data has a binomial distribution?

I need help testing that data has a binomial distribution? I am not quite sure how to do this. Question as below: A hundred students take a test on which there are 5 questions, each to be answered simply yes or no. The number of students getting 0…
Sarah Jayne
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Real-life question: How to determine the winner of a quiz

Imagine there's a quiz on the internet intended for a wide audience. It contains a (unlimited) number of questions, all of them with yes/no answers. A person gets one random question and must answer it, after that he can get another one. He can…
Jeyekomon
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How to calculate projected value?

I am trying to figure out how to calculate a projected value for our goals. Each of our sales persons is assigned an annual goal for 2014, say 60 units. Let's say, as of today, one sales person has sold 5 units. How would I calculate, assuming…
mattruma
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Statistics：How to prove that one variable's change is influenced by another variable,that is to say ,they are related?

I major in Bioinformatics. Now,I am in a problem: we all know that temperature changes during a year , I find that a disease incidence is really high when temperature is relatively high , while it becomes really low when the temperature is…
wuchang
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Checking random number generators

Given a function: $$ f(x) = \begin{cases} ax^2 & \text{for } x\in [ -1, 1], \\0 & \text{for } x\notin [-1,1].\end{cases} $$ I am to create a random number generator. I did this by finding the CDF and so I end up with $$X = \sqrt[3]{2F-1}$$ (F being…
Straightfw
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How the step of squaring the deviations in Standard Deviation overcomes the drawback of ignoring the signs of mean deviation.

$$\text{Mean deviation from mean}=\frac1N\sum_{i=1}^nf_i|x_i-\bar x|$$and $$\text{Standard Deviation ($\sigma$)}=\sqrt{\frac1N\sum_{i=1}^nf_i(x_i-\bar x)^2}$$ The step of squaring the deviations in SD overcomes the drawback of ignoring the signs…
Silent
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The weighted mean results in smaller value than the simple mean.

If weights attached to larger items are smaller and those attached to smaller items are larger, then the weighted mean results in smaller value than the simple mean. My try: Let the weights be $w_1
Silent
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95 % confidence interval

In a random sample of 41 cyclists two years ago, 18 tested positive for drugs. A random sample of 45 is conducted this year and 15 test positive. (a) Give a 95 percent confidence interval for the percentage who tested positive two years ago. (b) Can…
alex
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