By Klotz J.H.

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Extra resources for A computational approach to statistics

Example text

If A ∈ A then Ac ∈ A. (iii). if Ai ∈ A for i = 1, 2, . . , ∞ then ∞ i=1 Ai ∈ A. Using (i) and (ii) we have φ = S c ∈ A. If Ai ∈ A for i = 1, 2, . . , ∞ then ∞ i=1 Ai ∈ A using DeMorgan’s rule and (ii),(iii) ∞ i=1 Ai = ( ∞ i=1 Aci )c ∈ A . 3. PROBABILITY Using the infinite sequence {Ai : i = 1, 2, . . , ∞} where Ai = φ for i = N + 1, N + 2, . . , ∞ we have using (iii) ∞ N Ai = i=1 i=1 Ai ∈ A . Then using this finite union, DeMorgan’s rule, and (ii),(iii) we have N N Ai = ( i=1 i=1 Aci )c ∈ A and finite unions and intersections belong to A as well as countably infinite unions and intersections.

04. An individual 56 CHAPTER 2. DISCRETE PROBABILITY tests positive for the disease. What is the probability that the person has the disease? Let B1 be the event that the person has the disease, B2 that the person does not, and A the event of being positive for the disease on the screening test. 0001 . 001917 . 17 larger than the population incidence. So don’t panic but follow it up. 1 Independent Events For the case when P (A|B) = P (A), that is knowing B has occurred does not affect the probability of A, we say that the events A and B are independent.

2) 46 CHAPTER 2. DISCRETE PROBABILITY where N (N ) S1 P (Ai ) = i=1 (N ) S2 = 1≤i