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# Lecture6_print - MA/STAT416 Probability Lecture Notes Spring 2011 1 Chapter 4 Discrete Random Variables and Mass Functions 4.1 Mass Function and

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MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 4: Discrete Random Variables and Mass Functions February 18, 2011 4.1 Mass Function and Mode of a Random Variable Deﬁnition 1. The mode is the most probable value; the value with the highest proba- bility. Deﬁnition 2. Let X be a discrete random variable taking the values x 1 ,x 2 , ··· . The probability mass function of X is deﬁned by p ( x ) = P ( X = x ), where x = x 1 ,x 2 , ··· . Note p ( x ) = 0 otherwise. 4.2 CDF and Median of a Random Variable Deﬁnition 3. The cumulative distribution function CDF of a random variable X is the function F ( x ) = P ( X x ). Deﬁnition 4. Given the CDF F ( x ) for X . Any number m such that P ( X m ) 0 . 5 and P ( X m ) 0 . 5 is called a median of X . The median is not unique. 4.3 Examples Example 5 . A fair coin is tossed twice. Let X be the number of heads. Find the pmf of X . Example

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## This note was uploaded on 04/23/2011 for the course STAT 416 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lecture6_print - MA/STAT416 Probability Lecture Notes Spring 2011 1 Chapter 4 Discrete Random Variables and Mass Functions 4.1 Mass Function and

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