4. Suppose X(t) is a Brownian motion process without drift, o2 = 4 and X (0) = 0. = (a) It is known that X(10) = 5, what
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4. Suppose X(t) is a Brownian motion process without drift, o2 = 4 and X (0) = 0. = (a) It is known that X(10) = 5, what
4. Suppose X(t) is a Brownian motion process without drift, o2 = 4 and X (0) = 0. = (a) It is known that X(10) = 5, what is the probability that X(18) is between 8 and 12? [8 marks] (b) It is given that X (20) = 18, calculate the probability that X(7) is less than 3. [8 marks] 2 (c) Calculate the probability that the minimum of X(t) during 0 < t < 6 is not more than -9. [8 marks]
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