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sol.HW3 - EE 7615 Solutions to Problem Set 3 4.3 We need...

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EE 7615 Solutions to Problem Set # 3 4.3 We need that R 1 be sufficient statistic for decisions about S ∈ { s 1 , s 2 } = { E, - E } based on ( R 1 , R 2 ). For this we need p R 2 | R 1 ,S ( r 2 | r 1 , s ) = p R 2 | R 1 ( r 2 | r 1 ) s ∈ { s 1 , s 2 } , r 2 , r 1 The event that S = s and R 1 = r 1 is the same as the event that S = s and N 1 = r 1 - s . Therefore we need p N 2 | N 1 ,S ( r 2 - r 1 | r 1 - s, s ) = p 1 p R 2 | R 1 ,S ( r 2 | r 1 , s 1 )+ p 2 p R 2 | R 1 ,S ( r 2 | r 1 , s 2 ) s, r 2 , r 1 where p 1 = P ( S = s 1 ) and p 2 = P ( S = s 2 ). Now the signal S is independent of the noise components. Therefore we can write p N 2
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  • Fall '11
  • Naragipour
  • SEPTA Regional Rail, Pennsylvania Railroad locomotives, The Signal, Pennsylvania Railroad, Subaru R1, r2 |r1

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