Question: Let W(t) be a standard Wiener process and let X(t) be defined as X(t) = W(t) tW(1), 0 t 1. 1. Calculate, E[X(t)], the expectation

Let W(t) be a standard Wiener process and let X(t) be defined as

X(t) = W(t) tW(1), 0 t 1.

1. Calculate, E[X(t)], the expectation of Z(t).

2. Give the expression of E[X(t)X(s)].

3. Give the expression of the variance of X(t).

4. Is X(t) a WSS process? Is X(t) a strict stationary process? Justify your answers.

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