Monte-Carlo Integration

Description

This lecture covers Monte-Carlo integration, focusing on random variables, simulation, and calculating integrals using spreadsheets and Python. It explains how to generate draws from different distributions and transform them for various applications.

In MOOCs (2)

Instructor

Official source

https://mediaspace.epfl.ch/media/0_t17oiyt6

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A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product is a product distribution. The product distribution is the PDF of the product of sample values. This is not the same as the product of their PDF's yet the concepts are often ambiguously termed as "product of Gaussians".

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Complex random variable

In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.

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