Math 385 Exam 1
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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
