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Let X(t) and Y (t) be independent standard Brownian motions. (a)Show that Z(t) = X(t) Y(t) is a Brownian motion. What is the variance parameter

Let X(t) and Y (t) be independent standard Brownian motions.

(a)Show that Z(t) = X(t) Y(t) is a Brownian motion. What is the variance parameter for Z(t)?

(b) True or False: With probability one, X(t) = Y (t) for infinitely many values of t. Explain your answer.

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