DMP 7.4: Conditional Probability and Independence

Reading

Read Section 1.4, pages 29–36, and Section 1.5, pages 43–46.

The main notions are:

• Conditional probability
• The multiplication rule
• The law of total probability
• Bayes' Theorem
• Independence.

Incidentally, the reverend Thomas Bayes was a statistician, philosopher, and minister who came to Edinburgh to study logic and theology in 1719. Bayes' theorem is the basis for all of statistics and machine learning. The Bayes Centre, next to the Informatics Forum, is named after him.

Video

To get a feel for conditional probabilities, the multiplication rule, and the law of total probability, the following video walks through Exercise 55.

Exercises

For practice, you can try your hand at the following representative exercises: 50, 54, 61, 63, 64, 71, 75, 82, 91, and 99. (You will get the idea halfway, and don't have to make them all!)