Introduction to Probabillity and Data - Week 3

Video 1 - Introduction

Overlap and Preview

 

Video 2 - Disjoint Events + General Addition Rule

 

1. Disjoint/Non Disjoint Events

  Disjoint Events : both cases cannot happen at the same time(ex: tail and head)

  Non Disjoint Events : cases that can happen at the same time

 

2. General Addition Rule

  P(A∪B) = P(A) + P(B) - P(A∩B) (For disjoint events, P(A∩B) = 0)

 

3. Sample Space : a collection of all possible outcomes of a trial

 

4. Probability Distributions : 

 

5. Complementory events : Disjoint Event + all Probability of events adds up to 1

  

Video 3 - independence

 

independence : two processes are independent if knowing the outcome of one provides no useful information of an outcome of the other.

* Checking for independence : If P(A|B) = P(A), A and B are independent

 

If A and B are independent, P(A∩B) = P(A) * P(B)

 

disjoint & independent :

1) disjoint : cannot happen at the same time → P(A∩B) = 0

2) independent : knowing the outcome of one provides no useful information about the other → P(A|B) = P(A)

 

Video 4 - marginal, joint, conditional probability

 

Bayes' Rule : If A has occured, the probability of B occur is given as below.

P(A|B) = P(A∩B) / P(B)

* 여기서 P(B)가 0인 경우는 어떻게 되는가?

so, by changing the formula a little bit, we can make a new general multiplication rule.

P(A∩B) = P(A|B) * P(B)

 

Video 5 - Probability Trees

 

* It is effecient to use probability trees when considering conditional probabilities.

 

posterior probability vs p-value