MATH 180A Discussion 1

Events are subsets of the sample space

Inclusion Exclusion Principle

Note:

6-sided fair die


A := is even
B = is a multiple of 3
C = is odd

Disjoint

are disjoint

uniform

Case I: …Contradiction
Case II: …Contradiction
Can’t have a uniform distribution on
Furthermore you can’t have a uniform distribution on (use integral magic)

cumulative distribution function
CDF PDF by differentiation
PDF CDF by integration
where is the probability distribution function

Geometric distribution





What is the probability that I never get a 6?
Let’s call this event





Geometric series