Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

Statistical inference makes propositions about a population using data sampled from the population. To test a hypothesis about a population, a typical workflow is to select a statistical model of the process that generates the data and then deduce propositions from the model.

Statistical propositions include—

  • a point estimate, which is a particular value that best approximates some parameter of interest,

  • an interval estimate, for example, a confidence interval (or set estimate), which is an interval constructed using a data set drawn from a population so that, under repeated sampling of such data sets, such intervals would contain the true parameter value with the probability at the stated confidence level,

  • a credible interval, which is a set of values containing, for example, 95% of posterior belief,

  • rejection of a hypothesis, or

  • clustering or classification of data points into groups.

3930 questions
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Why does the inner product represents the variability of a random variable?

I am studyng about the $R^2$ coeficient in a OLS regression. I would like to understand the following statement: One measure of the variability of the dependent variable $y$ is the sum of squares: $$y'y = \langle y,y \rangle = \sum_i^n y_i^{2}$$ I…
Fam
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What type of drawn sample is more informative about $\theta$?

We have two sampling methods: 1. $X_1,\ldots,X_n$ from a Bernoulli$(\theta)$ distribution; 2. $Y_1,\ldots,Y_n$ from a Geom($\theta$) distribution. Which is more informative about $\theta$ and also what would you choose if the sample size $n$ is…
Mr. Bromwich I
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How does the Doomsday argument make any sense?

I just don't understand the Doomsday argument at all. As Wikipedia tells it, you say that "I'm 95% likely to not be one of the first 5% people to be born", and then because of that multiply the number of people born so far by 20 and claim a 95%…
Superbest
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Approximation in Central Limit Theorem

I have a question like this. There are $50$ people in a line. The time takes to serve a person has a mean of $5$ mins and standard deviation of $3$ mins. $5$ people can be served at a time. What is the probability that $50$ people can be served…
Padmal
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Pareto distribution confidence interval

$X$ is distributed by Pareto with $$f_X (x) = \frac{\alpha k^{\alpha}}{x^ {\alpha +1}},\alpha,k>0,x>k.$$ Derive a 95% confidence interval for $k $. My friend said I gotta do this $$Pr (x_{0.025} \leq \frac{k}{\hat k} \leq x_{0.975})= 0.95 \tag…
John Istabull
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What is the difference between $\sigma, \sigma_{\bar{x}}, S, s,$ and $s_{\bar{x}}$?

What is the difference between $\sigma, \sigma_{\bar{x}}, S, s,$ and $s_{\bar{x}}$? My textbook uses lots of different symbols, and it's not clear to me what the difference between all of them are. Are they just the same?
larrysummersstatistics
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Find probabilities given moment generating function.

The moment generating function of $X$ is $$m(t)= \exp( -6t+32t^2)$$ Find A. $\;\;P(-4
Smith Pay
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Uniformly Most Powerful

Let X1;X2; : : : ;X10 denote a random sample of size 10 from a population which has an exponential distribution with parameter ; > 0, i.e. with pdf f(x) =   e x if x 0; 0 otherwise. (a) Find the Uniformly Most Powerful Test (UMP) test of size …
AMG
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a complete sufficient statistic in geometric distribution

Exponential family has a very good property that could be used to conclude if a statistic is complete: $X_1,X_2,\ldots,X_n$ are from exponential family which has the form as: $$f(x\mid \theta )=h(x)c(\theta )e^{\sum_{i=1}^k w_i(\theta…
Liz Sugar
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95% Confidence interval of proportion test without calculator

I need some help regarding a calculation that I need to be able to do only with a basic calculator of a proportion test: A statistician is choosing a sample of 200 seeds. If 155 of these 200 are growing, what is the 95 confidence interval of the…
XCoder
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Statistical inference

Ten balls are picked without replacement from a box of 50 balls. All turn out to be red. A argues that the box contains only red balls. B argues that it contains 25 balls each of red and and some other colour. And in the pickings of the balls,…
Seetha Rama Raju Sanapala
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Confidence Intervals with two variables

A random sample of $50$ men shows the following relation between annual income $Y$ (in dollars) and education $X$ (in years): estimator for $Y, (\hat{Y}) = 1200 + 800X $ Average income is $Y = \$10,000$ and average education is $X = 11.0$ years.…
Alina P
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Bayesian inference for dependent data

Is it possible to use bayesian inference technique for data which does not follow the memoryless property? What is the likelihood function and prior in this case?
easternray
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Statistical Intervals - Confidence Intervals Homework Help

The following is a homework problem from my textbook, I am totally confused on how to solve this problem. Please help!!!!! Let $X_1, X_2, ………, X_n$ be a random sample from a continuous probability distribution having median μ~ (so that P(Xi ≤ μ~) =…
user133976
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Calculating expectation using Gamma and Exp R.V.'s

I'm working on a homework problem from Hogg (7.3.4) and am a bit stuck. I need to calculate the following expectation: $$ E(Y) = \int^{\infty}_0 \frac{2}{\theta}y e^{-\frac{y}{\theta}}(1-e^{-\frac{y}{\theta}}) dy$$ Breaking this up into 2 integrals,…
asahi
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