Chapter04 - Continuous Random Variables • A continuous...

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Unformatted text preview: Continuous Random Variables • A continuous random variable can take on values from an entire interval of the real line. • The probability density function (pdf) of a continuous random variable, X , is a function f ( x ) such that for a < b • The cdf of X is defined as ( ) ( ) b a P a X b f x dx &#2; &#0; = &#2; ( ) ( ) ( ) x F x P X x f t d t- &#0; = &#0; = Some relationships • What is the relationship between f and F ? • P ( a ≤ X ≤ b ) = F ( b ) – F ( a ) • P(X = a) = P ( a ≤ X ≤ a ) = F ( a ) – F ( a ) = 0 Pipeline example • A pipeline is 100 miles long and every location along the pipeline is equally likely to break • Let X be the distance measured in miles from the pipeline origin where a break occurs • What is the cdf for X ? • What is the pdf for X ? • What is P(30 ≤ X ≤ 50)? Requirements of a pdf • A pdf must satisfy the following two requirements: • Does the pipeline pdf satisfy these requirements? ( ) 0 for all ( ) 1 f x x f x dx &#2;- &#0; = Uniform distribution • A uniform distribution on the interval from A to B , U ( A , B ), is defined by a pdf of the form • Does f ( x ) meet requirements?...
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This note was uploaded on 10/14/2008 for the course STAT 211 taught by Professor Parzen during the Spring '07 term at Texas A&M.

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Chapter04 - Continuous Random Variables • A continuous...

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