4. The random process Z(t) is defined by Z(t) = 2Xt - Y, where X and Y are two correlated random variables with means m_X and m_Y, variances ??_X^2 and ?_Y^2, and correlation coefficient ?. Find (a) The mean function of Z(t) (b) The auto-covariance function of Z(t)
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The mean function is given by the expected value of Z(t): E[Z(t)] = E[2Xt - Y] Since the expected value is a linear operator, we can separate the terms: E[Z(t)] = 2E[Xt] - E[Y] Now, we know the means of X and Y are m_x and m_y, respectively. So, E[Z(t)] = Show more…
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