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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online