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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Problem 5
Let {X(t), t ≤ R} and {Y(t), t ≤ R} be two independent random processes. Let Z(t) be defined
as
Z(t) = X(t)Y(t), for all t = R.
Prove the following statements:
a. μz(t) = μx (t) uy (t), for all tER.
b. Rz(t₁, t2) = Rx (t₁, t2) Ry (t₁, t2), for all t = R.
c. If X(t) and Y(t) are WSS, then they are jointly WSS.
d. If X(t) and Y(t) are WSS, then Z(t) is also WSS.
e. If X(t) and y(t) are WSS, then X(t) and Z(t) are jointly WSS.

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