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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central limit theorem using expected value

Considerable controversy has arisen over the possible aftereffects of a nuclear weapons test conducted in Nevada in 1957. Included as part of the test were some three thousand military and civilian "observers". Now, more then fifty years later,…
notamathwiz
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Calculating mean and standard deviation for a set

Suppose we have a set $A = \{a_1, a_2, a_3, a_4, a_5\}$ where $a_n \in \mathbb{R}$ and a set $B = \{b_1, b_2, b_3, b_4, b_5\}$ where $b_n \in \mathbb{R}$ and a set $C = \{ma_1 + nb_1, ma_2 + nb_2, ma_3 + nb_3, ma_4 + nb_4, ma_5 + nb_5\}$ where $m,…
astiara
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Basic Math Question I think...

I apologize for the title. I am not even sure how to phrase this question per se. I feel like this should be easy and yet I am questioning my thinking. Here's the scenario: I have two groups. Group A has 50 members. Group B has 400 members. …
bossjimmark
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Samping from a Bivariate Normal Distribution

Consider the following bivariate normal distribution: $N((1,0), \textbf{I})$. When we sample $10$ means from this distribution, how exactly does this work? Is each mean a linear combination of $\mu_1 = 1$ and $\mu_2 = 0$?
guesguy
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Consistent estimator of mean/ Proof Correction

Let be a random variable $X$ with normal distribution $X\sim N (\mu, \sigma^2)$ and observations $x_1, x_2, · · ·, x_N$ come from a simple random sample. Prove that $\hat{\mu} = \sum_{n=1}^N \frac{x_n}{N-1}$ is a consistent estimator of the…
Gabriel Granda
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Positive parameters for Gamma random variables

I am sorry for the poor quality of this question: For $\Gamma(\alpha,\beta)$ random variables, why do we assume $\alpha>0$ and $\beta>0$?
ernesto
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Finding a set of data points from scratch, to satisfy conditions of mean and standard deviation

A question asked me to find a set of data points (numbers) with mean $50$ and standard deviation $8.75$ and it can be any number of data points. My best attempt was guess and check, using $50$ and one value above and one value below (the different…
user71207
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Mode of wickets taken gets two modes

The Data Collected I came across a situation where i got 2 modes, 0 and 1. Now thats probably the answer but 0 wickets dont mean anything anything in the logical sense as 10 players took no wickets while other 10 players did take a wicket. Do i have…
Lenicyl
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Where is $[1-F(a-\theta)]^{n_{2}}$ from in likelihood?

As an example, suppose $X_{1}, X_{2}, \ldots, X_{n_{1}}$ are iid with pdf $f(x-\theta)$, for $-\infty<$ $x<\infty$, where $-\infty<\theta<\infty$. Denote the cdf of $X_{i}$ by $F(x-\theta) .$ Let $Z_{1}, Z_{2}, \ldots, Z_{n_{2}}$ denote the censored…
ALEXANDER
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Use the method of moments to estimate the occurrence rate

A criminologist is searching through FBI files to document the prevalence of a rare double-whorl fingerprint. Among six consecutive sets of 100,000 prints scanned by a computer, the numbers of persons having the abnormality are 3, 0, 3, 4, 2, and 1,…
notamathwiz
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Finding unknown values given cumulative distribution for set of data.

I am confused on the correct answers to this problem. The data is given by the age of the first 44 presidents upon inauguration…
ernesto
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Question on statistics - mean and standard deviation?

I'm not sure what to do here: A class of 30 students were weighed. Their mean was found to be 58kg with a standard deviation of 5.5kg. What percentage of students will have a mass between 52.5 kg and 63.5 kg?
missiledragon
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Expectation of Pearson Chi-square divergence

Following the highly-cited paper, "Estimation of Entropy and Mutual Information" (Liam Paninski, link at the end), it is mentioned that the expectation of Pearson's chi-square functional (divergence) equals to, \begin{equation*} E_{p}\left[ \chi…
MBt
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Joint density function of iid exponential distribution?

Let random variables $X_1$, $X_2$ and $X_3$ be independent and identically distributed according to the exponential distribution with rate $\lambda$. Let $Y_1 = X_1$, $Y_2 = X_1 + X_2$, and $Y_3 = X_1 + X_2 + X_3$. (a) Find the joint density…
Adam Mac.
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Calculating the area of a rectangle taking uncertainties into account.

Take a rectangle with length $A \pm a$ and width $B \pm b$. Taking the max value as $(A+a)(B+b)$ and min value as $(A-a)(B-b)$ and uncertainty range as $(max-min)/2$ we get the formula: $$Area=(AB+ab)\ \pm (Ab+aB)$$ I find the presence of the $ab$…
Kantura
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