01_16 - STAT 410 Examples for discrete continuous If Spring...

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STAT 410 Examples for 01/16/2008 Spring 2008 discrete continuous If x x p x g all ) ( ) ( < , E ( g ( X ) ) = x x p x g all ) ( ) ( If ± - x x f x g d ) ( ) ( < , E ( g ( X ) ) = ± - x x f x g d ) ( ) ( variance Var ( X ) = 2 X = E ( [ X - μ X ] 2 ) = E ( X 2 ) – [ E ( X ) ] 2 discrete continuous Var ( X ) = ( ) - x x p x all 2 X ) ( ± = [ ] 2 all 2 ) X ( E ) ( x x p x - Var ( X ) = ( ) ± - - x x x d f ) ( 2 X ± = [ ] 2 2 ) X ( E ) ( x x x d f - ² ² ³ ´ µ µ · ± - Example 1 : x p ( x ) x 2 p ( x ) 1 0.2 0.2 2 0.4 1.6 3 0.3 2.7 4 0.1 1.6 E ( X 2 ) = 6.1 Var ( X ) = 6.1 – 2.3 2 = 0.81 6.1 Example 2 : f X ( x ) = ¸ ¹ ¸ º » < < o.w. 0 1 0 3 2 x x E ( X 2 ) = ± 1 0 2 2 3 x x x d = ± 1 0 4 3 x x d = 5 3 . Var ( X ) = E ( X 2 ) – [ E ( X ) ] 2 = 2 4 3 5 3 ¼ ½ ¾ ¿ À Á - = 80 3 .
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Example 4 : Suppose a discrete random variable X has the following probability distribution:
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01_16 - STAT 410 Examples for discrete continuous If Spring...

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