A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so that the amplifiers output is Y = AS. Assume that the random variables A and S are independent. It is known that the random gain is either 3 or 7, with P{A = 3} = 0.8.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
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A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so that
the amplifiers output is Y = AS. Assume that the random variables A and S are independent. It is
known that the random gain is either 3 or 7, with P{A = 3} = 0.8.
Transcribed Image Text:A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so that the amplifiers output is Y = AS. Assume that the random variables A and S are independent. It is known that the random gain is either 3 or 7, with P{A = 3} = 0.8.
Characterize the transformation g: IR→IR that can be applied to the output Y in or-
der to estimate the unknown signal S from the data Y such that the mean-square error,
E[lg(Y) S2], is minimized.
Transcribed Image Text:Characterize the transformation g: IR→IR that can be applied to the output Y in or- der to estimate the unknown signal S from the data Y such that the mean-square error, E[lg(Y) S2], is minimized.
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