STA_Notes_8.31.07

# STA_Notes_8.31.07 - B{HHH,TTH,THT,HTT o B can have 1 or 3...

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STA Class 04:02:10 3.2 Unions and Intersections o These are compound events —they are formed by the composition of two or more other events o Union (A U B)—event that occurs if either A or B or both occur on a single performance of an experiment. Union o Fig 3.2-1 Intersection (fig 3.2-2) o Event that occurs if both A and B occur (fig 3.2-3) Ex. Our experiment will consist of tossing a fair die once. o Let A = getting an even number o Let B = getting a number greater than 4 Find: (fig 3.2-4) 3.3 Complementary Events o The complement of an event A is that A does not occur o Notation: A^c ^ = to the power of o P(A^c) = 1 – P(A) o Fig 3.2-5 P(A^c) + P(A) = 1 P(A^c) = 1 – P(A) o Ex. A fair coin is tossed 3 times and events A and B are defined A: {at least one head} B: {# of heads observed is odd}

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STA Class 04:02:10 Find: P(A^c) Find: P(B^c) A: {HHH,HHT,HTH, THH, TTH, THT, HTT}
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Unformatted text preview: B: {HHH,TTH,THT,HTT} o B can have 1 or 3 so P(B) = 4/8 • P(A^c) = 1 – (7/8) = 1/8 • P(B^c) = 1- (4/8) = ½ • 3.4 Additive Rule and Mutually Exclusive Events o AdditiveRule: Fig 3.4-1 Why is it necessary to subtract out (fig 3.4-2)? Ex #1 Drug Testing • Find (fig 3.4-3) Need: P(A), P(B), and (fig 3.4-2) • Table for drug test (fig 3.4-4) • Mutually Exclusive o If (Fig 3.4-5) = ø, then A and B are said to be Mutually exclusive and (fig 3.4-2) = 0 o Ex. Toss a fair die once. Define: event A = (numver greater than 5) Define EDvent B = (odd number) Are A and B mutually exclusive? **Important Note: if A and B are Mutually Exclusive, then (fig 3.4-3) = P(A) + P(B) STA Class 04:02:10 • A = {6} B = {1, 3, 5} Fig 3.4-6...
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STA_Notes_8.31.07 - B{HHH,TTH,THT,HTT o B can have 1 or 3...

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