Question We are given the following random process r(t) = Arect(tB – 1/2) U(0, c1) and B ~U(1/c4, 1/c2) and the random variables A and B are indepen- dent. (a) Determine E[r(t)]. (b) Determine the autocorrelation of r(t), Rx(T). (c) Determine the PSD of x(t), Sx(f). (d) Assume now that this random process signal is passed through a system with the impulse response h(t) = rect(t/c4) to give the output y(t). Determine Ely(t)]. (e) Determine the variance of y(c4). (f) Determine Sy(f). (g) Determine Ry (T). Try to get an expression as simple as possible.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.1: Measures Of Center
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It is about a random process.

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We are given the following random process
r(t) = Arect(tB – 1/2)
where A - U(0, c1) and B ~U(1/C4, 1/c2) and the random variables A and B are indepen-
dent.
(a)
Determine E[r(t)].
(b)
Determine the autocorrelation of r(t), Rx(T).
(c)
Determine the PSD of x(t), Sx(f).
(d)
Assume now that this random process signal is passed through a system with
the impulse response
h(t) = rect(t/c4)
to give the output y(t).
Determine E[y(t)].
(e)
Determine the variance of y(c4).
(f)
Determine Sy(f).
(g)
Determine Ry (T). Try to get an expression as simple as possible.
Transcribed Image Text:Question We are given the following random process r(t) = Arect(tB – 1/2) where A - U(0, c1) and B ~U(1/C4, 1/c2) and the random variables A and B are indepen- dent. (a) Determine E[r(t)]. (b) Determine the autocorrelation of r(t), Rx(T). (c) Determine the PSD of x(t), Sx(f). (d) Assume now that this random process signal is passed through a system with the impulse response h(t) = rect(t/c4) to give the output y(t). Determine E[y(t)]. (e) Determine the variance of y(c4). (f) Determine Sy(f). (g) Determine Ry (T). Try to get an expression as simple as possible.
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