South Dakota School of Mines & Technology Expectations for Exponential

South Dakota School of Mines & TechnologyExpectations for Exponential

 2  1   x   x e dx  0  ( 2 ) 1     2  Expected Life For a producted governed by an exponential life distribution, the expected life of the product is given by  2.0   x E [ x]  x  e dx  1.8 1.6 1.4 0 1.2   x f (x t )   e 1.0 Density 0.8 0.6 0.4 0.2 X 0.0 0 0.5 1 1.5 2 2.5 3 1/

  ( x   ) 2 dF ( x )  2  E [( x   ) 2 ] =    2  ( x   ) 2 p ( x ) x   2  ( x   ) 2 f ( x ) dx   Variance

  2  ( x   ) 2 f ( x ) dx    ( x 2  2 x    2 ) f ( x ) dx  2  x f ( x ) dx  2  xf ( x ) dx   2 f ( x ) dx    Property

 2  E [ X 2 ]   2 1  2  x 2  e   x dx  ( ) 2    1 3  1   x   x e dx    2 0  ( 3 ) 1 1     2 3  2  Exponential Example For a producted governed by an exponential life distribution, the expected life of the product is given by 2.0 1.8 1.6 1.4 1.2   x f (x t )   e 1.0 Density 0.8 0.6 0.4 0.2 X 0.0 0 0.5 1 1.5 2 2.5 3 1/ =

South Dakota School of Mines & Technology Expectations for Exponential