1. The continuous time Gaussian process x has zero mean and autocorrelation a) Find P [x(T 1 ) >…

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1. The continuous time Gaussian process x has zero mean and autocorrelation
a) Find P [x(T1) > 1] and P [x(T1) > x(2T1)], with T1 = 1/(8f0).
b) Write the expression of the average PSD of x.
2. Let s(t) be a Gaussian random process with zero mean and PSD
The process is filtered by a filter with frequency response
With  Compute the probability that the amplitude of the signal at the filter output, y(t), lies in the range [−0.6, 0.6].
 

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