# 14SumsofVRs - Click to edit Master subtitle style EE 3180...

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Unformatted text preview: Click to edit Master subtitle style EE 3180 Probability and Sum of Two RVs Jeffrey B. Burl EE 3180 Probability and 11 EE 3180 Probability and The Sum of Two RVs n Given the sum of two RVs: n Example: Radar time of arrival. EE 3180 Probability and 22 Z X Y = + 2 m n R t t c = + EE 3180 Probability and Moments n The expected value of a sum is: n The variance of the sum is: EE 3180 Probability and 33 [ ] [ ] [ ] E Z E X E Y = + ( 29 ( 29 2 2 [ ] Var Z E Z Z E X Y X Y =- = +-- ( 29 ( 29 ( 29 ( 29 2 2 2 E X X E X X Y Y E X Y X Y =---- + +-- 2 2 [ ] 2 x y xy Var Z = +- EE 3180 Probability and The Distribution Function n The probability distribution function is: n The distribution function can be found from the joint density function by integrating of the region shown: EE 3180 Probability and 44 ( ) Pr( ) Pr( ) Z F z Z z X Y z = = + , ( ) ( , ) z y Z X Y F z f x y dxdy X--- = x+y=z x y EE 3180 Probability and...
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## This note was uploaded on 06/16/2010 for the course EE ee3180 taught by Professor Burl during the Spring '10 term at Michigan Technological University.

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14SumsofVRs - Click to edit Master subtitle style EE 3180...

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