Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Elements of Statistics: Estimation & Distributions

Description

This lecture covers the fundamental concepts of statistics, including elements of estimation theory, distributions, and the law of large numbers. Topics include random variables, moments, covariance, correlation, random processes, central limit theorem, and error analysis. Practical examples illustrate the application of these concepts in various fields.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

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 distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

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".

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Related lectures (49)

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Probability and Statistics

Covers probability, statistics, independence, covariance, correlation, and random variables.

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Related concepts (32)

Normal distribution

Probability distribution

Random variable

Statistics

Estimation theory