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Unformatted text preview: ISYE 2028 Exam 1 Equations Dr. Kobi Abayomi March 25, 2009 You must show all work to receive full credit. All regrades must be submitted the day the exam is returned. 1 Information You May Find Useful : Functions of One Random Variable Given a random variable X , defined with probability mass function p X : F ( x ) = X all t x p X ( t ) P ( a X b ) = X a t b p X ( t ) = X all X xp ( x ) = X all X x P ( X = x ) = E ( X ) V ar ( X ) = 2 = E [( X ) 2 ] = E ( X 2 ) [ E ( X )] 2 Given a random variable X , defined on the real line R , with probability density function f X : F X ( x ) = Z x f X ( t ) dt P ( a X b ) = Z b a f ( x ) dx X = Z R xf ( x ) dx = E ( X ) 2 X = E [( X ) 2 ] = Z ( x ) 2 f ( x ) dx = V ar ( X ) = V ar ( X ) = E ( X 2 ) 2 Functions of Multiple Random Variables For jointly continuous X,Y F X,Y ( x,y ) = P ( X x,Y y ) dF X,Y ( x,y ) = f X,Y ( x,y ) 2 f X  Y ( x  y ) = f X,Y ( x,y ) f Y ( y ) = P ( X...
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 Spring '07
 SHIM

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