In electrical engineering, the unwanted “noise” in voltage or current signals is often modeled by a Gaussian (i.e., normal) distribution. Su

Question

In electrical engineering, the unwanted “noise” in voltage or current signals is often modeled by a Gaussian (i.e., normal) distribution. Suppose that the noise in a particular voltage signal has a constant mean of 0.9 V, and that two noise instances sampled τ seconds apart have a bivariate normal distribution with covariance equal to 0.04e–jτj/10. Let X and Y denote the noise at times 3 s and 8 s, respectively. (a) Determine Cov(X, Y).

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Samantha 2 weeks 2021-09-14T23:30:13+00:00 1 Answer 0

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    2021-09-14T23:31:24+00:00

    Answer:

    Cov(X, Y) =0.029.

    Step-by-step explanation:

    Given that :

    The noise in a particular voltage signal has a constant mean of 0.9 V. that is μ = 0.9V …………(1)

    Also, the two noise instances sampled τ seconds apart have a bivariate normal distribution with covariance.

    0.04e–jτj/10 …………(2)

    Having X and Y denoting the noise at times 3 s and 8 s, respectively, the difference of time = 8-3 = 5seconds.

    That is, they are 5 seconds apart,

    τ = 5 seconds…………..(3)

    Thus,

    Cov(X, Y), for τ = 5seconds = 0.04e-5/10

    = 0.04e-0.5 = 0.04/√e

    = 0.04/1.6487

    = 0.0292

    Thus, Cov(X, Y) =0.029.

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