Homework assignment 5 (due November 7)
A probability space is a triple (W, A, Pr) consisting of an arbitrary non-empty set of worlds or possibilities
W, an algebra A of propositions over W, and a probability measure Pr: A→ ℜ.
A probability measure Pr: A → ℜ is a function from the algebra of propositions Ainto the real numbers
ℜ such that for all B and C in A:
(1) Pr(B) ≥ 0.
(2) Pr(W) = 1.
(3) Pr(B∪C) = Pr(B) + Pr(C) if B∩C = ∅.
If Pr(C) > 0, the conditional probability of B given C, Pr(B|C), is defined as Pr(B∩C)/Pr(C).
If Pr(C) = 0, the conditional probability of B given C, Pr(B|C), is not defined.
Show that the following claims hold true in a probability space (W, A, Pr).
Claim I: For all B in A, Pr(B) = Pr(B|W). (1 point)
Claim II: For all B in A, Pr(B|B) = 1 if Pr(B) > 0. (1 point)
Claim III: Pr(∅) = 0. (1 point)
Claim IV: For all B in A, Pr(B) = 1 – Pr(W\B). (1 point)
Claim V: For all B and C in A, Pr(B) = Pr(B∩C) + Pr(B∩(W\C)). (1 point) (Hint: use (IV) from homework
assignment 1)
Homework assignment 6 (due November 14)
Claim VI: For all B and C in A, Pr(B∪C) = Pr(B) + Pr(C) – Pr(B∩C). (1 point) (Hint: use (IV) and (VIII) from
homework assignment 1)
Claim VII: For all B and C in A, Pr(B∩C) = Pr(B)xPr(C|B), whe

More
Less