**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Normal Distribution: Properties and Calculations

Description

This lecture covers the properties and calculations related to the normal distribution, including the standard normal density, quantiles, and transformations. It explains how to calculate probabilities, expectations, and variances for normal random variables. Examples are provided to illustrate the concepts, such as determining probabilities for specific scenarios and finding quantiles of normal distributions.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Instructors (2)

In course

MATH-232: Probability and statistics

A basic course in probability and statistics

Related concepts (167)

Statistics

Statistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Probability axioms

The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .

Summary statistics

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.

Mathematical statistics

Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling.

Related lectures (1,000)

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Probability and StatisticsMATH-232: Probability and statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Probability and StatisticsMATH-232: Probability and statistics

Covers fundamental concepts in probability and statistics, including distributions, properties, and expectations of random variables.

Interval Estimation: Method of MomentsMATH-232: Probability and statistics

Covers the method of moments for estimating parameters and constructing confidence intervals based on empirical moments matching distribution moments.

Modes of Convergence of Random VariablesMATH-232: Probability and statistics

Covers the modes of convergence of random variables and the Central Limit Theorem, discussing implications and approximations.