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09 Midterm Review-1

# Σ n 1 i 2 i 1 n x x s n 1 i 2 i 100 x s cv 100 μ σ

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σ N 1 i 2 i = - = 1 - n ) x (x s n 1 i 2 i = - = 100% x s CV = 100% μ σ CV =

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The Basics and Rules of Probability 15 Probability Likelihood or chance that a particular event will occur Basic Terminology Experiment: A process producing a single outcome whose result cannot be predicted with certainty Elementary outcome: A unique outcome of an experiment Event: Set of elementary outcomes of interest Sample Space: Set of all possible elementary Assigning Probabilities Classical Probability Assessment: All outcomes equally likely to occur Relative Frequency of Occurrence: Based on actual observations Subjective Probability Assessment: Based on opinion or judgment
The Basics and Rules of Probability 16 Rule 1: Probability of any elementary outcome must fall in the interval from zero to one Rule 2: Probabilities for all elementary outcomes in an experiment (the sample space) must sum to one Additive Rule: For any two events A and B P(A or B) = P(A) + P(B) – P(A and B) Venn Diagrams 0 P ( e i ) 1 = S in outcomes elementary all 1 ) ( i e P

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The Basics and Rules of Probability 17 Complement of A (Ac or A’ or A) = Not A Probability of all areas which are not part of A Intersection (A and B) = Area where both A and B are true Probability of A and B = P(A ∩ B) Called “joint” probability Union (A or B) = Area where either A or B are true Probability of the combined area of A and B = P(A U B) Mutually Exclusive = no overlap between events For mutually exclusive events, the intersection is always zero: P(E 1 E 2 ) = P(E 1 ) + P(E 2 ) - P(E 1 E 2 ) = P(E 1 ) + P(E 2 )
The Basics and Rules of Probability 18 Conditional Probability: Probability of A given B = P(A|B) Multiplicative Rule: P(B) B) P(A B) | P(A = A) | P(A)P(B B) | P(B)P(A B) P(A = =

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19 The Basics and Rules of Probability Bayes’ Rule Revising probability of events after receiving new information For two events: A and B Joint probability of A and B Total probability of B ) A | )P(B A P( A) | P(A)P(B A) | P(A)P(B P(B) B) P(A B) | P(A + = =
20 The Basics and Rules of Probability Independence: Two events are independent if the occurrence of one event has no effect on the probability that the other event occurs. If A and B are independent, and P(A)>0 and P(B)>0 Mutually exclusive events are not independent! To show independence, sufficient to show one of these are equivalent P(B) P(A) B) P(A A) | P(B P(A) P(B) B) P(A B) | P(A = = = = P(A)P(B) B) P(A =

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Example 21 A US-based manufacturer sources one of its most critical components from two different suppliers, one in Malaysia and one in Mexico. Due to various reasons, such as labor strikes, equipment failure or pandemic diseases, both of the suppliers are subject to production disruptions. When a supplier faces a disruption, it cannot satisfy the manufacturer’s orders for components; hence, the manufacturer relies on the supplier who does not face a disruption.
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σ N 1 i 2 i 1 n x x s n 1 i 2 i 100 x s CV 100 μ σ CV...

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