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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What's the probability of a future polling result falling in a given range?

Question Each day, Gallup polls U.S. Employee Engagement. You can see 7-day rolling averages of the daily numbers here. Assume you have a set of historical daily numbers (ie, [0.354827, 0.352648, 0.34943, …]). What would be the best technique to…
Aaron Brager
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What is the distribution of an average of independent Poisson random variables?

If I have random variables $X_1,X_2,\ldots,X_n$ that are Poisson distributed with parameters $λ_1,λ_2,\ldots,λ_n$, what is the distribution of $Y=1/n \sum X_i$? Who knows this can give an answer because I don't know how to do, please.
denny
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NFC SuperBowl coin toss hot streak --> hypothesis testing and power calculation

There are many Q&A's on SE related to coin tossing - the simplest stochastic process. My Q is about relating mathematics and statistics to what in biomedicine and healthcare is termed "evidence" based on real world data. In 46 SuperBowls, NFC teams…
alancalvitti
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Geometric mean of 2 sets

If $2$ finite sets of positive integers have different cardinality but the same arithmetic mean, does the set with the greater number of elements always have a lower geometric mean?
Simon
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Finding new standard deviation and mean after adding an element

Say I have a mean and standard deviation for a dataset of 5 elements. I now add a sixth element. Is there a way to calculate the new mean and standard deviation using the information we had prior (i.e. not just recalculating the whole thing from…
MT_
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When do I use a z-score vs a t-score for confidence intervals?

I have a set of 1000 data points. I would like to estimate their mean using a confidence interval. I read somewhere that if the sample size, $n$, is bigger than 30 you should use a t-score, and else use a z-score. Is that true?
Demetri Pananos
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Mode of lognormal distribution

Suppose $$y=e^{x}$$ where x is normal with mean mu and variance sigma. Then I see how to derive mode of f(y) (distribution of y), as we need to find the value y that makes $$f'(y)==0$$ However, why is mode not simply $$e^{\mu}$$? y is a monotonic…
user2465355
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Intuition behind Fisher information and expected value

I am learning stats. On page 128 of my book, All of Statistics 1e, it explains that the Fisher information is the variance of the score function. It then goes on to say that when $n = 1$ $$I(\theta) = -E_{\theta}\left(\frac{\partial^2 \log\space…
bernie2436
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Bivariate Normal Distribution Problem vs Marginals

If $X_1 \sim N(0,1)$ and $X_2 \sim N(X_1^2, 1)$ then does $(X_1, X_2)$ follow a bivariate normal distribution? My thinking is that $X_1 ^2$ is $\chi^2_1 $ since it's the square of a $N(0,1)$ random variable. And then since $X_2$ has a $\chi^2_1$ as…
Robert B
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Mean and Variance of Methods of Moment Estimate and Maximum Likelihood Estimate of Uniform Distribution.

Let $X_1, X_2,\ldots, X_n$ be i.i.d. uniform on $[0, \theta ]$. a. Find the method of moments estimate of $\theta$ and its mean and variance b. Find the MLE of $\theta$ and its mean and variance. Thank you for answering, I really appreciate it.…
Kaji
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Why is the "wrong" interpretation of confidence intervals still seemingly correct?

According to online sources, if you are operating at 95% confidence, it means if you repeated a sampling process many times and then looked at the 95% confidence intervals over all the results, 95% of the time the brackets would contain the true…
AJJ
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Multivariate Moment Generating Function

Let $X$ and $Y$ be two independent random variables both have Laplace distribution. What is the moment generating function of $U=X+Y$ and $V=X-Y$? Initially, I want to work out the $f_{U,V}(u,v)$, and then work out the…
John
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Over-determined and Under-determined systems

How do I show that a system is both over-determined and under-determined? I am supposed to come up with a matrix that satisfies both but am not really sure I understand what types of equations would satisfy these criteria. If anyone could give me an…
Marie
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Fitting a sine wave of known frequency through three points

We have a computationally expensive function of a large set of data and an angle, that is known to result in a sine wave: $$ f(\text{data}, \theta) \approx a \sin (\theta + b) + c$$ We want to find the constants $a$, $b$, and $c$, executing the…
rabbidrabbit
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Does the ratio $\mathrm{Var}(x)/E(x)$ have any statistical meaning?

I am wondering how to compare the volatility of two sets of samples. Can I consider the ratio $\mathrm{Var}(x)/E(x)$ as a normalized variance?
Rein
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