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Electrical and Computer Engineering

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a) Suppose Xt is a random process which is second-order stationary. Show that it is also stationary of order 1.

b) Show that if X and Y are independent then they are also uncorrelated.

c) If events A and B are disjoint then they are also independent. True or False?

d) If X and Y are jointly Gaussian then Z = root(x^2 + y^2) is also Gaussian. True or False?

f) If Pxy = 1 then y = ax + b for some a > 0. True or False?

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Solution contains true/false answers and full explanations on electrical and computer engineering.

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(a) The first order stationary random process has the following feature:
E[Xt]=mu for all t ----> mean is time independent.

The second order stationary random process has the following features:
E[Xt]=mu for all t
E[Xt^2]=mu2 for all t ----> mean and variance are time independent.
Cov[Xt, Xs] is only a function of t-s.

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