Week4Solutions - RANDOM PROCESSES IN COMMUNICATION...

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σµ µ XX X EX 22 2 2 =−= {( ) } { } xfxd x ba xd x x b a a b a b {} ( ) () 2 3 33 11 3 1 3 1 3 == = = =+ + −∞ ∫∫ RANDOM PROCESSES IN COMMUNICATION ASSIGNMENT #4 PROBLEM 2.23 fx X , = 1 axb << , elsewhere X = 0 a b a b X x f xd x xdx x = = = 2 2 1 2 2
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[] σµ XX EX b a ba b a b a b a b a o r a b 22 2 2 2 2 32 2 2 1 3 1 2 333 1 4 2 4 1 4 1 12 2 1 12 1 12 =− = + + + =++− + = {} ( ) ( ) () PROBLEM 2.29 fx y XY , (,) , = 1 2 0 ≤≤ xy 02 y a) for and f x y d y d y yx Y x x , == = = −∞ 1 2 2 2 2 0 y , fy f x y d x d x YX Y y y , , = = ∫∫ 1 2 0 0 0 y b) y y y y Y / , (/) / / = 12 2 1 for , 0 y
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for fy x fx y x x YX XY X | , (|) (,) () / == = 12 1 2 1 2 00 2 ≤≤ xy y , c) Find EXY a n dEXY {| } . } 10 5 x f xyd x x y dx y x y yy y y y y y y {|} ( |) . . } . } | . = = = −∞ = = ∫∫ 11 2 1 22 1 2 1 2 05 2 1 4 0 2 0 2 1 d) y . () , =− = 1 1 2 These are not equal, therefore X and Y are not statistically independent .
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This note was uploaded on 10/13/2010 for the course MATH MATH 2255 taught by Professor Landis during the Spring '10 term at Fairleigh Dickinson.

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Week4Solutions - RANDOM PROCESSES IN COMMUNICATION...

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