Lecture1_9_Review

Lecture1_9_Review - ECE 340 Probabilistic Methods in...

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1 ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 1_9: Review Lecture 1_9: Review
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2 Review Section 2.1 Examples of experiments Sample Space & Examples Discrete Continuous Events & Examples Certain event Null event Set Operations •U n i o n Intersection Complement
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4 Properties of Probability a. Many times, occur can S ways of # occur can A ways of # ) ( ) ( ) ( S N A N A P = Relative frequency of percentage b. Properties i. For an event A, P(A) = 1 – P(A)’ P(A’) = 1 – P(A) ii. If 2 events, A & B are mutually exclusive, then P(A B) = 0. iii. For 2 events A & B, P(A B) = P(A) + P(B) – P(A B) iv. For 3 events A, B, C P(A B C) = P(A) + P(B) + P(C) – P(A B) – P(A C) - P(B C) + P(A B C)
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5 Probability Theory Some Probability Laws Commutative Laws: A B = B A A B = B A Associative Laws: (A B) C = A (B C) (A B) C = A (B C) Distributive Laws: A (B C) = (A B) (A C) A (B C) = (A B) (A C) De Morgin’s Laws: (A B)’ = A’ B’ (A B)’ = A’ B’
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6
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7 Review Section 2.3 Counting Sampling w/ & w/o replacement Permutations of n objects
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8 Enumeration or Counting Technologies Summary With Replacement Without Replacement Order relevant (ab ba) n 1 × n 2 ×… n r )! ( !
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This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture1_9_Review - ECE 340 Probabilistic Methods in...

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