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**Unformatted text preview: **.75 + e – .075 ) = 1.078( – .472 + .928) = .491. 4.2 Cumulative distribution functions and expected values The cumulative distribution function Definition The cumulative distribution function F ( x ) for a continuous rv X is defined for every number x by F ( x ) = P ( X x ) = °±?²³? ? −∞ If X is uniform on [A,B], its cdf is 2 Proposition Let X be a continuous rv with pdf f ( x ) and cdf F ( x ). Then for any number a , P ( X > a ) = 1 – F ( a ) and for any two numbers a and b with a < b , P ( a X b ) = F ( b ) – F ( a ). Example 7 Proposition If X is a continuous rv with pdf f ( x ) and cdf F ( x ), then at every x at which the derivative F ( x ) exists, F ( x ) = f ( x )....

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