Math 385 Exam 1

De Morgan's Law

(A ∩ B)c = Ac ∪ Bc (A ∪ B)c = Ac ∩ Bc

P(∅)

= 0

P(A)

= |A|/|Ω|

Monotonicity

If A ⊆ B, then P (A) <= P (B)

Pairwise Disjoint

P (A ∪ B) = P (A) + P (B)

Union Rule

P (A ∪ B) = P (A) + P (B) − (A ∩ B)

Complement rule

P(Ac) = 1−P(A)

Continuous Probability

P(A|B) =

probability mass function (pmf)

f(x) = P(X = x) Properties: ◦ f(x) ≥ 0 for all x. ◦ ∑ f(x) = 1. ◦ If A is an event then