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Course# MATH-232: Probability and statistics

Summary

A basic course in probability and statistics

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Instructors (2)

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Related concepts (417)

Advanced statistical physics

We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.

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Random variate

In probability and statistics, a random variate or simply variate is a particular outcome of a random variable; the random variates which are other outcomes of the same random variable might have different values (random numbers). A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). Random variates are used when simulating processes driven by random influences (stochastic processes).

Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

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.

Merge sort

In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.

Lectures in this course (49)

Permutations and Binomial CoefficientsMATH-232: Probability and statistics

Explains permutations, binomial coefficients, and multinomial coefficients with practical examples.

Probability and StatisticsMATH-232: Probability and statistics

Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

Combinatorial MathematicsMATH-232: Probability and statistics

Explores combinatorial mathematics, covering permutations, combinations, and binomial coefficients, along with probability and statistics concepts.

Probability and Statistics for SICMATH-232: Probability and statistics

Delves into probability, statistics, random experiments, and statistical inference, with practical examples and insights.

Probability and StatisticsMATH-232: Probability and statistics

Introduces key concepts in probability and statistics, illustrating their application through various examples and emphasizing the importance of mathematical language in understanding the universe.