Probability

view on github

• Sample Space
• Permutations and Combinations
• Binomial and Multinomial Distribution
• Bayes Rule
• CDF, PDF, PMF
• Maximum Likelihood Estimation

---

Sample Space

• random variable: is a function from sample space into the real numbers
• $\sigma-algebra$

• Power set

Permutations and Combinations

• Vandermonde Identity

Binomial and Multinomial Distribution

• connection to hypergeometric distribution: binomial is with replacement, and hypergeometric is without replacement.

Bayes Rule

• Prior

• Posterior

• Conditional Independence

Events $A$ and $B$ are conditional independence give $C$ if

$$P(A\cap{B}\|C)=P(A\|C)P(B\|C)$$

Example: Chess Competition, if you play chess with an opponent. It may happen that the games are conditional independent but not independent.

• Short form

• w/o without
• w/ with
• b/c because

CDF, PDF, PMF

• Cumulative Density Function
• Probability Density Function
• Probability Mass Function

Maximum Likelihood Estimation