# OpenStax CNX

##### Sections
You are here: Home » Content » Introduction to Statistics

### Recently Viewed

This feature requires Javascript to be enabled.

# Introduction to Statistics

Collection type: Course

Course by: Ewa Paszek. E-mail the author

Note: You are viewing an old version of this content. The latest version is available here.

## Collection Properties

Summary: Introduction to Statistics. Random Variable, Mean, Variance, Standard Deviation and Mathematical Expectation. Discrete Distributions: Bernoulli trials and Bernoulli distribution, geometric distribution, Poisson distribution. Continuous Distributions: random variables of the continuous type, uniform distribution, exponential distribution, gamma distribution, chi-square distribution, normal distribution, t-distributions. Estimation: biased and unbiased esimators, convidence intervals for means, convidence intervals for varinces, sample size, maximum error of the point estimate, Likelihood function, Maximum Likelihood Estimation (MLE), Asymptotic Distributions of Maximum Likelihood Estimators, Chebyshev’s Inequality. Hypothesis: tests of statistical hypotheses, Type I error, Type II error, tests about proportions, null hypothesis, alternative hypothesis, significance level of the test, probability value, tail-end probability, standard error of the mean, tests about one mean and one variance, test of the equality of two independent normal distributions, best critical region, Neyman-Pearson Lemma, most powerful test, uniformly most powerful critical region, Likelihood Ratio tests, critical region for the likelihood ratio test. Pseudo-Numbers: uniform pseudo_random variable generation, congruential generators, shift-register generators, Fibonacci generators, Combinations of Generators (Shuffling). The Inverse Probability Method for Generating RandomVariables. The Logistic Distribution.

Instructor: Marek Kimmel

This collection contains: Modules by:

## Content actions

### Give feedback:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks