L08_S10 - AMS 311, Spring Semester 2010 Lecture 8 Chapter...

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AMS 311, Spring Semester 2010 Lecture 8 Chapter Four: Random Variables 4.1. Random Variables Definition : Let S be the sample space of an experiment. A real-valued function R S X : is called a random variable of the experiment if, for each interval } ) ( : { , I s X s R I is an event. Definition: If X is a random variable, then the function F defined on ) , ( -∞ by ) ( ) ( t X P t F = is called the cumulative distribution function of X. Some authors use the term distribution function rather than cumulative distribution function (cdf ). 4.2. Discrete Random Variables For a discrete random variable X , we define the probability mass function (pmf) ) ( a p of X by }. { ) ( a X P a p = = Example 2a. The probability mass function of a random variable X is given by , , 2 , 1 , 0 , ! ) ( = = i i c i p i λ where . 0 Find } 0 { = X P and }. 2 { X P 4.3. Expected Value Definition The expected value of a discrete random variable X with the probability function ) ( x p and set of possible values
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L08_S10 - AMS 311, Spring Semester 2010 Lecture 8 Chapter...

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