P5 - Multiple random variables

When dealing with multiple random variables that are not independent. We need their joint probability mass (or density) functions. With these we can calculate probabilities, marginal probability mass (or density) functions, and expectations including covariance and correlation.

Central Limit Theorem: part 1: https://youtu.be/xSNg9Vp1wko part 2: https://youtu.be/Q11BS_wnq3w

Probability playlist: https://www.youtube.com/playlist?list=PLFHD4aOUZFp1FxJs9BG5Sbsy6NvCO3Qb1

STAT 587: https://www.jarad.me/courses/stat587Eng/ STAT 587 Videos: https://www.jarad.me/courses/stat587Eng/slides/ Slides: https://www.jarad.me/courses/stat587Eng/slides/Probability/P5-Multiple_random_variables/P5-Multiple_random_variables.pdf

00:27 - Joint probability mass function 01:11 - CPU example 01:57 - CPU example - outcomes 03:59 - CPU example - joint pmf 05:42 - CPU example - probabilities 07:00 - Expectation 07:44 - CPU example - expected absolute speed difference 08:50 - Marginal probability mass function 10:44 - CPU example - independence 12:20 - Covariance 13:03 - CPU example - covariance 14:01 - Correlation 14:28 - Correlation interpretation 15:45 - CPU example - correlation 16:04 - Continuous random variables 18:34 - Continuous random variables - independence 19:09 - Properties of variance and covariances 20:25 - Summary

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