Let X(t) be a zero-mean WSS Gaussian random process with Rx(t) = e¯¹². Suppose that X(t) is input to an LTI system with transfer function |H(ƒ)| = e¯¾¹f² Let Y(t) be the output. a. Find My. b. Find Ry (T) and Var(Y(t)). c. Find E[Y(3)|Y(1) = −1].
Let X(t) be a zero-mean WSS Gaussian random process with Rx(t) = e¯¹². Suppose that X(t) is input to an LTI system with transfer function |H(ƒ)| = e¯¾¹f² Let Y(t) be the output. a. Find My. b. Find Ry (T) and Var(Y(t)). c. Find E[Y(3)|Y(1) = −1].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Problem 19
Let X(t) be a zero-mean WSS Gaussian random process with Rx(t) = e¯¹². Suppose that X(t) is
input to an LTI system with transfer function
| H(f)| = e = ²/²f²
Let Y(t) be the output.
a. Find My.
b. Find Ry (T) and Var(Y(t)).
c. Find E[Y(3)|Y(1) = −1].
d. Find Var(Y(3)|Y(1) = -1).
e. Find P(Y(3) < 0|Y(1) = −1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47f6c1da-c6df-426c-81ec-6020162a0815%2Fd265c1b2-7947-41b0-a6aa-71cbdb5b6461%2F2yefwnq_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 19
Let X(t) be a zero-mean WSS Gaussian random process with Rx(t) = e¯¹². Suppose that X(t) is
input to an LTI system with transfer function
| H(f)| = e = ²/²f²
Let Y(t) be the output.
a. Find My.
b. Find Ry (T) and Var(Y(t)).
c. Find E[Y(3)|Y(1) = −1].
d. Find Var(Y(3)|Y(1) = -1).
e. Find P(Y(3) < 0|Y(1) = −1).
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