Now someone has used intuition to guess an answer for Part a as 92(Y) = 5Y/31. Ex-plain where this guessed answer may have come from and comment on the optimality of theguessed estimator 92. 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.

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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or
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In this problem, we consider target detection in a radar system. Upon observing a realization a of the random variable X which represents the return signal in noise, a decision has to be made as to whether the target is present or absent. The target amplitude is known and equal to A > 0. The observation is made in zero-mean Gaussian noise W whose variance is known and equal to 2. If the target is present (hypothesis H1), X = A+W. If the target is absent (hypothesis Ho), X = W . The likelihood ratio test for this problem is stated as follows: If fi (x)/fo(x) > n= decide in favor of H1; otherwise, decide in favor of Ho.lf n = 1, determine the probability of correct detection (target declared present when indeed present) and the probability of false alarm (target declared present when in fact absent). Express these probabilities in terms of the ratio a = A/o. If a = 4, which of the following represents the correct probabilities of false alarm and correct detection, respectively? O None of…
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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.