Mathematics Stack Exchange
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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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sum of rounding errors

My tax return involves 32 different numbers, each rounded to the nearest dollar and then added together. Assuming that the errors by rounding are uniformly distributed on the interval (-1/2,1/2), estimate the probability that the sum of the rounded…
user111230
  • 139
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Variance of a MLE $\sigma^2$ estimator; how to calculate

Let $X_1, X_2,...,X_n$ be an i.i.d. random sample from $N(0, \sigma^{2})$. a. Find the variance of $\hat{\sigma}^{2}_{MLE}$ So I found $\hat{\sigma}^{2}_{MLE}$ by taking the derivative of the log of the normal pdf function, but from there I am not…
user3325193
  • 155
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$95\,\%$ confidence interval for geometric distribution

I am analyzing data with a geometric distribution. Using maximum likelihood estimation, I can estimate $p$ to be $\displaystyle \hat p_{MLE} = \frac{N}{\sum_{i=1}^N x_i}$, where $N$ is the number of datapoints and each $x$ is the number of trials…
user3183724
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Confidence intervals for the variance. What if data is not normally distributed?

I am writing an essay about confidence intervals for the variance and there is a lot of information available under the assumption that our data is normally distributed, but there is not much said about other possible distributions. How can we find…
Karlis Olte
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Multiple regression degrees of freedom $f$-test.

I'm finding conflicting information from college textbooks on calculating the degrees of freedom for a a global $F$-test on a multiple regression. To be absolutely clear, assume there are 50 observations and 3 independent variables. Can you please…
MARK GOLDMAN
  • 41
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Why do p-values include the probability of obtaining more extreme values than the test statistic?

p-value is defined as "the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true". Why are all values more favourable to the alternative hypothesis than the one…
user117322
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Is the median always between the mode and the mean for a unimodal distribution?

Is it ALWAYS the case that, for a unimodal probability distribution, the median is between the mode and mean?
Mike Jones
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How can I find the median of this frequency distribution

How can we find out the median of a frequency distribution table?In fact, if you use a particular formula,it will be very kind of you to prove it(That's what I am really looking forward to) Thank you. Class boundary 60-70 70-80 80-90 …
Eisen
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Product of 2 Binomial distributions

I was wondering what the distribution is of the product of two binomial distributed random variables, X and Y; So suppose X ~ Bin(n,p1) and Y ~ Bin(n,p2) (so the number of experiments n is the same), what can we say about the distribution of XY? I…
user111663
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Find a transformation such that the Fisher Information is constant in terms of the parameter.

Say you have a Gamma distribution with parameters $\alpha$ known and $\theta$ unknown. Find a transformation of $\theta$, $\eta=g(\theta)$ such that ${\cal I} (\eta)$, the Fisher Information, is constant in terms of $\eta$. My problem is that the…
ActuariallyImpaired
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Margin of error and $98\%$ confidence interval question for stats people :)

The question is (this is homework, for an online class, no teacher so at times confusing) Carl conducted an experiment to determine if there is a difference in mean body temperature between men and women. He found that the mean body temperature for…
shari
  • 61
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Statistics of Lists

To start, let me say i am a programmer and not a math wiz, so this question might be very simple. I have a data set of prices that sort of looks like this 1399.00 13.99 13.97 13.83 13.48 ... ~9 So what happens is everyone "bids" a few cents lower…
Mike Buck
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Why is Wolfram giving me a different answer for standard deviation?

I have the following set of data: Raw Scores x-x̄ (x-x̄)² ----------------------------- 7 -6 36 8 -5 25 10 -3 9 14 1 1 26 13 …
Ayvadia
  • 143
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order statistics

I would like to understand the relationship between the asymptotic moments of order statistics and the moments of the distribution of the mother distribution. I will appreciate any references on this matter.
user12847
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Range of coefficient of Skewness

Prove that Pearson's second measure of Skewness that is Skewness = 3(Mean - Median)/Standard deviation lies between -3 and +3
linear
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