1. Let B = (B₁)tzo be a standard Brownian motion started at zero, and let (FB)zo denote the natural filtration of B. (1.1) State the definition of B. (1.2) Determine whether (B₁/√t) defines a standard Brownian motion. Explain your answer. t>0 (1.3) Show that T = inf {t≥0: B = 1+sin(t)} is a stopping time with respect to (FB) >0.

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A: As per our guidelines we are supposed to answer only one question. If you want solution of any…