Let W(t) be the standard Brownian motion. a. Find P(-1 < W(1) < 1). b. Find P(1 < W(2) + W(3) < 2). c. Find P(W(1) > 2|W(2) = 1).
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We want to find P(_1 < W(1) < 1). Since W(t) is a standard Brownian motion, we know that W(1) ~ N(0,1), where N(0,1) denotes a normal distribution with mean 0 and variance 1. Show more…
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