A stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain, A, so thatthe amplifiers output is Y = AS. Assume that the random variables A and S are independent. It isknown that the random gain is either 3 or 7, with P{A = 3} = 0.8. Calculate the mean-square error assuming that S is a {-1, 1, }-valued random variable withP{S=1}=0.6.

Given that stochastic signal S is amplified by an amplifier that has a stochastic, real-valued gain,…

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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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.