(1.5 hours to learn)
The conditional distribution of a random variable X given another random variable Y is the distribution of X when Y is observed to take some vaule. While the precise mathematical definition is involved, for discrete and continuous variables, it amounts to dividing the joint PDF or PMF of X and Y by the PDF or PMF of Y.
This concept has the prerequisites:
- Know the definitions of the conditional distribution for both discrete and continuous random variables
- For continuous random variables, why isn't it mathematically rigorous to condition on an event of probability zero?
- Know how the joint distribution of a set of random variables decomposes as a product of conditional distributions
Core resources (read/watch one of the following)
→ A First Course in Probability
An introductory probability textbook.
- Section 6.4, "Conditional distributions: discrete case," pages 288-291
- Section 6.5, "Conditional distributions: continuous case," pages 291-296
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 3.5, "Conditional distributions," pages 87-95
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 3.6, "Conditional distributions," pages 136-145
- We may be interested in whether two variables are independent conditioned on another random variable .
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