Question

(a) A Gaussian random process X(t) has zero mean and a power spectral density given below. Find the probability that X(t) takes a value outside the interval (-1.5 ... + 1.5). S_{XX}(?) 0.5? -2 -1 0 1 2 ? (b) The random process in (a) is affected by additive Gaussian white noise with zero mean and a variance of ?^2_{NN} = 0.25, resulting in a noisy process Z(t). The noise N(t) is independent from X(t). Find the probability that Z(t) takes a value outside the interval (-1.5 ... + 1.5).

          (a) A Gaussian random process X(t) has zero mean and a power spectral density given below. Find the probability that X(t) takes a value outside the interval (-1.5 ... + 1.5).
S_{XX}(?)
0.5?
-2 -1 0 1 2 ?
(b) The random process in (a) is affected by additive Gaussian white noise with zero mean and a variance of ?^2_{NN} = 0.25, resulting in a noisy process Z(t). The noise N(t) is independent from X(t). Find the probability that Z(t) takes a value outside the interval (-1.5 ... + 1.5).

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(a) A Gaussian random process X(t) has zero mean and a power spectral density given below. Find the probability that X(t) takes a value outside the interval (-1.5 ... + 1.5).
SXX(?)
0.5?
-2 -1 0 1 2 ?
(b) The random process in (a) is affected by additive Gaussian white noise with zero mean and a variance of ?^2NN = 0.25, resulting in a noisy process Z(t). The noise N(t) is independent from X(t). Find the probability that Z(t) takes a value outside the interval (-1.5 ... + 1.5).

Added by Peter F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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A Gaussian random process X(t) has zero mean and a power spectral density given below. Find the probability that X(t) takes a value outside the interval (-1.5 ... + 1.5). (b) The random process in (a) is affected by additive Gaussian white noise with zero mean and a variance of σ^2_NN = 0.25, resulting in a noisy process Z(t). The noise N(t) is independent from X(t). Find the probability that Z(t) takes a value outside the interval (-1.5 ... + 1.5).

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