Chap3 MTH3401

# Chap3 MTH3401 - Chapter 3 Random Variables and Probability...

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Chap 3 Random Variables and Probability Distributions 1 Chapter 3 Random Variables and Probability Distributions

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Chap 3 Random Variables and Probability Distributions 2 3.1 Concept of a Random Variable Random variable : is a function that associates a real number with each element in the sample space. Example 3.1 Two balls are drawn in succession without replacement from an box containing 4 red balls and 3 black balls. The possible outcomes and the values y of the random variable Y , where Y is the number of red balls, are Sample space y RR 2 RB 1 BR 1 BB 0
Chap 3 Random Variables and Probability Distributions 3 Concept of a Random Variable Definition 3.2: Discrete sample space : If a sample space contains a finite number of possibilities or an unending sequence with as many elements as there are whole numbers. Definition 3.3: Continuous sample space : If a sample space contains an infinite number of possibilities equal to the number of points on a line segment. Discrete random variable : If the set of possible outcomes of a random variable is countable. Continuous random variable : If a random variable can take on values on a continuous scale. Discrete random variables often represent count data The number of defectives, highway fatalities Continuous random variables often represent measured data Heights, weights, temperatures, distance or life periods

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Chap 3 Random Variables and Probability Distributions 4 3.2 Discrete Probability Distributions Frequently, it is convenient to represent all the probabilities of a random variable X by a formula . Probability function (probability mass function, probability distribution ) of the discrete random variable X : The set of ordered pairs . ) 3 ( ) 3 ( e.g., ); ( ) ( = = = = x P f x X P x f )) ( , ( x f x ) ( ) ( . 3 1 ) ( . 2 0 ) ( . 1 x x f x X P x f x f = = =
Chap 3 Random Variables and Probability Distributions 5 Discrete Probability Distributions Example 3.3 A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If a school make a random purchase of 2 of these computers. Find the probability distribution for the number of defectives. x 0 1 2 f ( x ) 28 3 2 8 0 5 2 3 ) 2 ( ) 2 ( 28 15 2 8 1 5 1 3 ) 1 ( ) 1 ( 28 10 2 8 2 5 0 3 ) 0 ( ) 0 ( = = = = = = = = = = = = X P f X P f X P f

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Chap 3 Random Variables and Probability Distributions 6 Discrete Probability Distributions Example 3.4 If a car agency sells 50% of its inventory of a certain foreign car equipped with airbags. Find a formula for the probability distribution of the
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Chap3 MTH3401 - Chapter 3 Random Variables and Probability...

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