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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Maximum likelihood estimators of three independent normal random variables with a common variance

Suppose that $X_1,\ldots,X_n$ are normal with mean $\mu_1$; $Y_1,\ldots,Y_n$ are normal with mean $\mu_2$; and $W_1,\ldots,W_n$ are normal with mean $\mu_1+\mu_2$. Assuming that all $3n$ random variables are independent, with a common variance, find…
woaini
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Inverse Gaussian, Limiting Distributions

I'm trying to understand the nature of limiting distributions and distributions, specifically $1/Z_n \longrightarrow ~?$ where $Z_n\longrightarrow Z -Gaussian(0,1)$ I understand that the gamma distribution converges to the gaussian for a large…
myTotoro
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Control Limits (stat)

An $\bar{x}$ chart is to be established based on standard values: $μ=600, σ=12, n=9.$ The control limits are based on $α$-risk of $0.01$. What are the appropriate control limits? $$\\$$ This is what I have so far: I know the mean/centerline =…
AmR
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How many people should be on a jury to be representative?

Assuming a jury is like a sample of a population. Assume the following: The population is a million people. There are X percent who think the defendant is guilty. Choose N random people to be a jury. Given X, how many jurors (what sample size) would…
zooby
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Expectation of CDF of standard normal distribution

How to calculate $E[\{\Phi(\alpha X)\}^{K}]$ for K being positive integer, $\Phi()$ is the CDF of standard normal distribution and $X\sim N(0,1)$. I tried using integration by part stuck.
Satya Prakash
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PDF from MGF inverse not triviAL

$$\frac{128 r t \, _1F_2\left(2;\frac{5}{2},\frac{7}{2};r^2 t^2\right)}{45 \pi } + \frac{2 r t+4 r t I_2(2 r t)-2 I_1(2 r t)}{r^3 t^3}$$ My computer and I found that this is the moment generating function of a distribution rooted in the geometric…
atat
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Does SSTR (sum of squares for treatments) = SSR (regression sum of squares)?

I'm on my first course into statistics and there seems to be something in common for Regression and ANOVA analysis: in ANOVA I'm told that SST (total sum of squares) = SSE(error sum of squares) + SSTR (sum of squares for treatments) while in…
user133466
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Best way to model reliability

I have 10 databases of facts from 10 different sources, I now know if the facts were true or false. What is the best way to form an equation to determine the reliability of each of the source? I don't want a source who got 4/4 True to have a higher…
gweno10
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Expectations Homework Questions Clarification

This is another one of the questions I didn't get a chance to ask the TA at my school today. I thought I had a pretty good grasp on Expectations but apparently I could still use some clarification. Hopefully someone can help me. Suppose that $n$…
CoderDake
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What is a population minimizer?

I am reading into statistics in combination with machine learning and I came across the expression "population minimizer". I found no good explanation on what a population minimizer exactly means, so what exactly is it?
uitty400
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sufficient statistic for a strange parameter on normal distribution

Let $X_1,\ldots,X_n$ identically indepedent and distributed like $N(b,1)$ . I'm supposed to find a sufficient statistic for $a=P[X_1<1]$.
Itried
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Which subject are these students best? (basic high school statistical question)

It's a very basic high school statistical question, but I'm struggling to solve it. Suppose I have a school with $287$ students and each one made a test with $50$ questions (multiple choice questions with $5$ items each, they have to choose one item…
user42912
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poisson distribution of chocolate

Let the number of chocolate drops in a certain type of cookie have a Poisson distribution. We want the probability that a cookie of this type contains at least two chocolate drops to be greater than 0.99. Find the smallest value of the mean that the…
user48495
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Which descriptive statistics are sufficient?

I was recently asked to choose from the basic set of descriptive statistics which ones are sufficient. Mean Median Mode Standard deviation E. Variance Range IQR (or IR) Skewness Kurtosis This was a test question, and I guess I…
zachd1_618
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Sufficient statistics

Suppose $T_1(X)$ is a sufficient statistic for $\theta$ for a family of distributions indexed by $\theta$ and $T_2(X)$ is another statistic that induces a “finer”(what is meant by a finer ? ) partition than $T_1$. How do I know that $T_2$ is also…
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