slide3 - ECON321 Econometrics Lecture 3 Discrete Random...

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ECON321 : Econometrics Lecture 3 : Discrete Random Variables and Probability Distributions Sasan Bakhtiari University of Maryland, College Park Summer 2007 Session II,
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Random Variable A variable that associates a number with each single outcome in Ω. Discrete random variable - A random variable whose possible values are from a discrete countable set X ∈ { 0 , 1 , 2 , 3 , 4 , 5 , 6 , . . . } Continuous random variable - A random variable whose possible values are drawn from one or a collection of continuous intervals. X [0 , 1] [2 , ] .
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Counting Techniques Consider a two-step operation 1. the first step can be done in n 1 ways, 2. the second step can be done in n 2 ways, The task can be done in n 1 × n 2 different ways. I Example: When flipping a coin twice the total number of outcomes is 2 × 2 = 4 { TT,TH,HT,HH }
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Counting Techniques Permutation Arranging n objects in different orders. I The number of permutations of n objects is n ! = 1 × 2 × . . . × n . I Example: three marbles with red, blue and green colors can be arranged in 3! = 6 different ways in a row { RBG, RGB, BRG, BGR, BRG, BGR }
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Counting Techniques Permutation Arranging a group of size r from n objects: The number of permutations of n objects is P n r = n ! ( n - r )! . I Example: There are 10 teachers and 6 classes to be taught. The classes can be taught in P 10 6 = 10! (10 - 6)! = 5040 different ways.
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Counting Techniques Combination When the order the objects are chosen does not matter, then choosing r objects from a total of n objects can be done in C n r = n !
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