08_25 - f X ( x ) = & &...

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STAT 410 Examples for 08/25/2008 Fall 2008 random variables discrete continuous probability mass function p.m.f. p ( x ) = P ( X = x ) probability density function p.d.f. f ( x ) x 0 p ( x ) 1 ( ) x x p all = 1 x f ( x ) 0 ( ) ± - x x f d = 1 cumulative distribution function c.d.f. F ( x ) = P ( X x ) ( ) x y y p ( ) ± - x d y y f Example 1 : x p ( x ) F ( x ) 1 0.2 0.2 2 0.4 0.6 3 0.3 0.9 4 0.1 1.0 F ( x ) = ² ² ² ³ ² ² ² ´ µ < < < < 4 1 4 3 9 . 0 3 2 6 . 0 2 1 2 . 0 1 0 x x x x x
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Unformatted text preview: f X ( x ) = &amp; &amp; &lt; &lt; o.w. 1 3 2 x x x &lt; 0 F X ( x ) = 0. 0 x &lt; 1 F X ( x ) = x d y y 2 3 = x 3 . x 1 F X ( x ) = 1. f X ( x ) F X ( x ) Example 3 : f X ( x ) = &amp; &amp; &gt;-o.w. 1 5 6 x x x &lt; 1 F X ( x ) = 0. x 1 F X ( x ) = -x d y y 1 6 5 = 1 5 x y-= 1 x 5 . f X ( x ) F X ( x )...
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08_25 - f X ( x ) = &amp;amp;amp; &amp;amp;amp;...

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