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
6
votes
2 answers

Convergence in probability

If $X_1, X_2, \ldots$ converge in probability to a constant $c$, then does $1-X_1, 1-X_2, \ldots$ converge in probability to $1-c$? Is there a way to show this is true / is there an already existent theorem for this?
MathMan
  • 1,319
6
votes
1 answer

How to explain if a quantity is a pivot quantity?

from what i have gathered . I know that pivots are functions that give approximate or exact assumption of CI . I'm not entirely sure what is the quantity the question is referring to. does the quantity mean the mean, standard deviation etc.?
user1919987
  • 197
  • 3
  • 6
  • 17
6
votes
2 answers

Why does the central limit theorem imply that the standard deviation approaches $\frac{\sigma}{\sqrt{n}}$?

According to the central limit theorem, if one takes random samples of size $n$ from a population of mean $\mu$ and standard deviation $\sigma$, then as $X$ gets large, $X$ approaches the normal distribution with mean $\mu$ and standard deviation…
David Faux
  • 3,425
6
votes
2 answers

Confidence interval of quotient of two random variables

I have random variables $X_1, X_2, \dots, X_n$ and $Y_1, Y_2, \dots, Y_n$, with $n$ a large integer. All pairs $(X_i, Y_i)$ are independent and identically distributed, but every $X_i$ and $Y_i$ within a pair are dependent. All $X_i$ and $Y_i$ yield…
Paul
  • 2,795
6
votes
1 answer

Maximum of beta-distributed random variables

Let $X_i \sim \operatorname{Beta}(\alpha_i, \beta_i)$ be independent beta-distributed random variables for $i = 1, \ldots, k$. What can we say about $$X =\max(X_1, \ldots, X_k)?$$ In particular, can we estimate $\alpha$ and $\beta$ so that $X$ is…
Jair Taylor
  • 16,852
6
votes
2 answers

Maximum likelihood estimator of categorical distribution

The task is: Population of the students has been divided into the following three groups: Students with the mean of grades below 3.5 Students with the mean of grades between 3.5 and 4.5 Students with the mean of grades above 4.5 Each student…
Yksisarvinen
  • 163
6
votes
4 answers

Intuition on variance of linear combination of variables

I have the formulas for the variance of linear combintion of variables given as $$ \text{Var}\Bigl(\,\sum_{i=1}^n X_i\,\Bigr)= \sum_{i=1}^n\text{Var}( X_i)+ 2\sum_{i< j} \text{Cov}(X_i,X_j). $$ I know this is derived from variance of 2 variables…
Jesse Meng
  • 1,310
6
votes
2 answers

Why $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$

I'm reviewing probability and statistics.The textbooks said that if the sampled population is infinite, then $$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$$ I'm curious about how does this result come from. Wikipedia does not tell me much. Is there…
Jill Clover
  • 4,787
6
votes
1 answer

Sufficient statistic for the Negative-Binomial Distribution

I am fairly new to this topic but here is my problem: I have stumbled across a paper (Robinson and Smyth, 2008) stating that the sample sum is a sufficient statistic for NB-distributed random variables. I have tried to verify this by using the…
Mark
  • 101
  • 1
  • 5
6
votes
5 answers

Benford's law with random integers

I tried testing random integers for compliance with Benford's law, which they are apparently supposed to do. However, when I try doing this with Python, map(lambda x:str(x)[0], [random.randint(0, 10000) for a in range(100000)]).count('1') I get…
Hypercube
  • 576
  • 1
  • 5
  • 14
6
votes
2 answers

Greatest common denominator of measurements

In a couple months, I'll do the Millikan experiment. Then, I'll end up with a number of charge measurements and their errors $$((q_i, \Delta q_i))_{i \in \mathbb N}.$$ The idea is that all those $q_i$ can be represented as a multiple of a fixed…
Martin Ueding
  • 4,523
6
votes
2 answers

Percentage greater than 2 standard deviations from the mean

A question reads: "The weights of $910$ young deer tagged and weighed in a research study are normally distributed with a mean of $86$ pounds and a standard deviation of $2.5$ pounds." Approximately how many deer weigh more than $91$ pounds? Since…
Haim
  • 757
6
votes
1 answer

Check answer, How to find Cov(x,y) and Var(2x-y)?

I have the following tableau x: -1 0 1 total y: 1 0 1/8 3/8 1/2 2 3/8 1/8 0 1/2 total: 3/8 2/8 3/8 1 *)Find Cov(x,y) and Var(2x-y) My work: I use…
Electro82
  • 1,146
6
votes
2 answers

Two envelope paradox, instead with amounts distributed uniformly.

There are two envelopes, each of which has a check for a Unif(0, 1) amount of money, measured in thousands of dollars. The amounts in the two envelopes are independent. You get to choose an envelope and open it, and then you can either keep that…
Spack Jarrow
  • 61
6
votes
3 answers

Why does Bayes Theorem work?

I have always wondered about the math behind Bayes Theorem because it looks really simple and seems like there's probably a simple explanation behind it. I don't understand the relationship between P(A and B) over P(B) and why this means "The…
WhatsInAName
  • 337
  • 2
  • 13
1 2 3
…
99 100