post10 - STAT 511-2 Spring 2012 Lecture 10 Feb 1 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 10 Feb 1, 2012 Jun Xie 3. Discrete random variables and probability distributions Random variables are numerical representations of outcomes of a random experiment. Definition For a given sample space S of some experiment, a random variable (rv) is any rule that associates a number with each outcome in S . Uppercase letters X, Y or Z denote random variables, lowercase letters x, y, or z denote the particular values of the corresponding random variables. Random variables are classified as discrete rv or continuous rv. 3.2-3.4 Probability distributions for discrete random variables The probability distribution or probability mass function (pmf) of a discrete rv is defined for every number x by p ( x ) = P ( X = x ) = P (all s S : X ( s ) = x ). The cumulative distribution function (cdf) F ( x ) of a discrete rv variable X with pmf p ( x ) is defined for every number x by F ( x ) = P ( X x ) = ±²³´ µ¶· , the probability that X will be at most x. Example 13
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post10 - STAT 511-2 Spring 2012 Lecture 10 Feb 1 2012 Jun...

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