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Unformatted text preview: Probability and Statistics Basic Probability concepts Most inspection and quality control theory deals with statistics to make inference about a population based on information contained in samples. The mechanism we use to make these inferences is probability. We use to represent the probability of any event (E) ( ) E P ( ) 1 E P ≤ ≤ The sum of all possible events = 1 P(S) = 1, S = Sample space Definition of Probability The ratio of the chances favoring an event to the total number of chances for and against the event. Probability Is always a ratio. P = Favoring not Chances Plus Favoring Chances Favoring Chances _ _ _ _ _ _ P(Event) = le_Space ts_in_Samp Total_Poin erest ent_of_Int _in_the_Ev ticipating Points_Par Number_of_ 1 Copy Right (c) Dr. Kai Yang Empirical Probability Empirical probabilities are nearly the only ones we know in industrial world. We watch and measure and count and calculate empirical probabilities from which we predict future probabilities. Also we stated that if an experiment is Repeated a large number of times, (N), and the event (E) is observed n E times, the probability of E is approximately: P(E) N n E ≈ Simple Events An event that cannot be decomposed is a simple event (E), or a sample point. The set of all sample points for an Experiment is called sample space (S) Compound Events Compound events are formed by a composition of two or more events. They consist of more than one point in sample Space. The two most important probability theorems are the additive and multiplicative laws. For the following Discussion, E A = A and E B = B. 2 Copy Right (c) Dr. Kai Yang I. Composition: A union or intersection of events A. Union of A and B. B A If A and B are two events in sample space (S), the union of A and B ( ) contains all sample points in event A Or B or both. B A B. Intersection of A and B. ( ). B A If A and B are two events in sample space (S), the intersection of A and B ( ) is composed of all sample Points that are in both A and B. B A II. Event relationships. There are three relationships in finding the probability of an event: Complementary, conditional and mutually exclusive. A. Complement of an event The compliment of an event A is all sample points in the sample space (S), but not in A. The compliment of A Is , and A P(A) 1 A P − = ) ( B. Conditional probabilities The conditional probability of event A given that B has occurred is: ) ( ) ( )  ( B P B A P B A P = If P(B) ≠ Two events A and B are said to be independent if either: P(AB) = P(A) or P(BA) = P(B) Otherwise, the events are said to be dependent 3 Copy Right (c) Dr. Kai Yang C. Mutually exclusive events If event A contains no sample points in common with event B, then they are said to be mutually exclusive....
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This note was uploaded on 05/09/2010 for the course IE IE7610 taught by Professor Dr.kaiyang during the Winter '10 term at Wayne State University.
 Winter '10
 Dr.KaiYang

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