X(t) is a wide sense stationary random process with average power equal to 1 Let 0 denote a random variable with uniform distribution over 0, 2 such that X(t) and 0 are independent (a) What is E X2(t) (b) What is E cos(2fct ) (c) Let Y(t) X(t)cos(2fct ) What is E Y(t) (d) What is the average power of Y(t)

Question: X(t) is a wide sense stationary random process with average power equal to 1. Let 0 denote a random variable with uniform distribution over [0,

X(t) is a wide sense stationary random process with average power equal to 1. Let 0 denote a random variable with uniform over [0, 2π] such that X(t) and 0 are independent.
(a) What is E[X2(t)]?
(b) What is E[cos(2πfct + ⊖)]?
(c) Let Y(t) = X(t)cos(2πfct + ⊖). What is E[Y(t)]?
(d) What is the average power of Y(t)]?

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