Question: Two stationary stochastic processes ????1???? and ????2???? have the following autocovariance functions: ????1???? ????0 = 0.5, ????1 = 0.2, ???????? =0 (???? 2) ????2????

Two stationary stochastic processes ????1???? and ????2???? have the following autocovariance functions:

????1???? ∶ ????0 = 0.5, ????1 = 0.2, ???????? =0 (???? ≥2)

????2???? ∶ ????0 = 2.30, ????1 = −1.43, ????2 = 0.30, ???????? =0 (???? ≥3)

Calculate the autocovariance function of the process ????3???? = ????1???? + 2????2???? and verify that it is a valid stationary process.

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