A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
A stochastic process (SP) X(t) is given by X(t) = Asin(ωt + Φ) where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π. a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2). c) Is X(t) wide sense stationary (WSS)? Justify your answer. Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) = 10e−1 4 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables. d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
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