MS-E1600 - Probability Theory D, 11.01.2021-22.02.2021
This course space end date is set to 22.02.2021 Search Courses: MS-E1600
Lecture 10: Random vectors and joint laws
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10.1 Random vector
A random vector is a list of random variables, measurable in a proper way.
10.2 Joint laws and marginals
The joint law of two or more random variables is a law of a random vector.
10.3 Multivariate densities
If a random vector admits a probability density function, then so do its coordinate variables. The converse is not true in general.
10.4 Laws of independence
The joint law of mutually independent random variables is a product measure.
10.5 Densities of independent random variables
Densities of independent random variables factorise almost everywhere.
10.6 Expectations of independent products
Under independence, the expectation of a product equals a product of expectations.
Alternative reading material
- [Jacod & Protter, Chapters 10 and 12]
- [Williams, Chapter 8]
Last modified: Thursday, 11 February 2021, 1:48 AM