Chapter2_427summary

Chapter2_427summary - Chap. 2: Basic Probability Outcome: a...

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1 Chap. 2: Basic Probability Outcome: a possible result Experiment: process leading to an uncertain outcome. Sample space S: set of all possible outcomes. Event: a subset of S. Probability measure (PM) is a function that assigns numbers between 0 and 1 to events.
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2 Rules for PM‟s 1. For any event A, P(A) > 0 2. P(S) = 1 3. Additivity: For any collection of disjoint events: A 1 , A 2 , …. we have that i.e., for disjoint events, Prob(union) = sum of individual prob‟s 1 1 ) ( i i i i A A P
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3 Basic properties of PM P(A ) = 1 – P(A) P( f ) = 0 If A is a subset of B, P(A) < P(B) P(A B) = P(A) + P(B) - P(A I B)
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4 Discrete Sample Space S = {E 1 , E 2 , E 3 , …. } For any event A, Special Case: Counting Problems S has N equally likely outcomes, so each has prob = 1 / N. Hence, P(A) = (# outcomes in A) / N ) ( ) ( A E i i E P A P
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1. Principle : If an operation consists of k steps, each of which can be done in n 1 , n 2 , …, n k ways, then the total number of operations
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Chapter2_427summary - Chap. 2: Basic Probability Outcome: a...

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