prob.part33.67_68

# prob.part33.67_68 - 2.2. CONTINUOUS DENSITY FUNCTIONS 59...

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2.2. CONTINUOUS DENSITY FUNCTIONS 59 Density Functions of Continuous Random Variables Defnition 2.1 Let X be a continuous real-valued random variable. A density function for X is a real-valued function f which satisFes P ( a X b ) = ± b a f ( x ) dx for all a, b R . ± We note that it is not the case that all continuous real-valued random variables possess density functions. However, in this book, we will only consider continuous random variables for which density functions exist. In terms of the density f ( x ), if E is a subset of R , then P ( X E ) = ± E f ( x ) dx . The notation here assumes that E is a subset of R for which ² E f ( x ) dx makes sense. Example 2.10 (Example 2.7 continued) In the spinner experiment, we choose for our set of outcomes the interval 0 x < 1, and for our density function f ( x ) = ³ 1 , if 0 x < 1, 0 , otherwise. If E is the event that the head of the spinner falls in the upper half of the circle, then E = { x : 0 x 1 / 2 } , and so P ( E

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## This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

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prob.part33.67_68 - 2.2. CONTINUOUS DENSITY FUNCTIONS 59...

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