Probability and Statistics Review for Artificial Intelligence, Machine Learning, Deep Learning

December 31, 2018

Topics

• 1. Probability Theory
• 2. Conditional Probability
• 3. Chain Rule
• 4. Bayes Rule
• 5. Discrete Random Variables
• 6. Continuous Random Variables

1. The Axioms of Probability

Consider an experiment whose sample space is . For each event E of the sample space we assume that a number E is defined and satisfies the following three axioms:

Axiom 1 states probability that the outcome of the experiment is an outcome in E is some number between 0 and 1.

$$0 \le P(E) \le 1$$

Axiom 2 states that with probability 1, the outcome will be a point in the sample space S.

$$P(S) = 1$$

2. Naive Definition of Probability

This is where I talk about Conditional probability.

3. Chain Rule

This is where I talk about chain Rule.

4. Bayes Rule

This is where I talk about Bayes Rule.

5. Discrete Random Variables

This is where I talk about Random Variables.

6. Continuous Random Variables

This is where I talk about Random Variables.