MSci_609_Discrete_Probability_Distributi

# MSci_609_Discrete_Probability_Distributi - DISCRETE...

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1/12/2011 1 DISCRETE PROBABILITY DISTRIBUTIONS INSTRUCTOR: AMER OBEIDI A variable is a characteristic (i.e., property, construct) of an individual population unit (subjects 2 of interest). The amount of flu vaccine in a syringe. The heart rate of an young baby. The time it takes a student to complete an examination. The barometric pressure at a given location. The number of registered voters who vote in a national election.

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1/12/2011 2 Random Variable variable that assumes numerical values associated 3 variable that assumes numerical values associated with random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point. Random variable: X A particular value in X is x It’s probability of occurrence is P ( X = x ) or P (x) Discrete random variable Whole number (0, 1, 2, 3, etc.) 4 Obtained by counting/listing. Usually a finite number of values. Poisson random variable is an exception (number per unit of measurement). Continuous Random Variable Random variable can take any numeric value (whole or f ti ) ithi f l i t l d i bt i d fraction) within a range of values or interval, and is obtained by measurement . Random variable that has an infinite number of distinct possible values (random number value is on a continuous scale).
1/12/2011 3 Random Possible 5 Experiment Variable Values Make 100 Sales Calls # Sales 0, 1, 2, . .., 100 Inspect 70 Radios # Defective 0, 1, 2, . .., 70 Count Cars at a Toll Between 11:00 & 1:00 # Cars Arriving 0, 1, 2, . .., Answer 33 Questions # Correct 0, 1, 2, . .., 33 Rd Pi b l 6 Experiment Random Possible Weigh 100 People Weight 45.1, 78, . .. Measure Part Life Hours 900, 875.9, . .. Amount spent on food \$ amoun 54 12 42 Measure Time Between Arrivals Inter-Arrival Time 0, 1.3, 2.78, . .. \$ amount 54.12, 42, . ..

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1/12/2011 4 Completely describes the random variable, denoted by P ( X = x ) or p ( x ). 7 1. List of all possible [ x , p ( x )] pairs x = value of random variable (outcome) p ( x ) = probability associated with that value 2 Mutually exclusive (no overlap 2. Mutually exclusive (no overlap) 3. Collectively exhaustive (nothing left out ) 0 p ( x ) 1 for all x p ( x ) = 1 8
1/12/2011 5 Listing Table 9 { (0, .25), (1, .50), (2, .25) } # Tails f( x ) Count p( x ) 01 . 2 5 12 . 5 0 21 . 2 5 Graph .50 p( x ) .00 .25 2 x Formula px n x!(n – x)! () ! = p x (1 – p) n - x An assembly line consists of three mechanical components Suppose that the probabilities that 10 components. Suppose that the probabilities that the first, second, and third components meet specifications are 0.95, 0.98, and 0.99, respectively. Assuming that the three components are independents, determine the probability mass function of the number of components in the assembly line that meet specifications.

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1/12/2011 6 X =Number of components that meet specifications. 11 {0 , ( ) 0 . 0 0 1 % } {1 , ( ) 0 . 1 6 7 % } {2 , ( ) 7 . 7 % } XP x x x     {3 , ( ) 9 2 . 1 % } x  Definition: F di t d i bl ith ibl 12 For any discrete random variable with possible values x 1 , x 2 , x 3 ,…, x n ; the events {X= x 1 }, {X= x 2 },{X= x 3 }…, {X= x n } are mutually exclusive.
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## This note was uploaded on 01/12/2012 for the course MSCI 609 taught by Professor Almehdawe,eman during the Fall '10 term at Waterloo.

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MSci_609_Discrete_Probability_Distributi - DISCRETE...

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