Let B(t) represent the change in the price (US dollars) of a barrel of crude oil t days from now. Suppose B(t) follows a Brownian motion with u = 0.01 and o = 0.15. 1. Find the probability that the price has changed by more than 1 dollar after 5 days. 2. Repeat the previous part but for 10 days. 3. Given that the price has increased by exactly 1 dollar in the first 7 days, find the conditional probability that it will be at least another dollar higher after an additional 7 days.

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Problem 2.
Let B(t) represent the change in the price (US dollars) of a barrel of crude oil t days from now. Suppose B(t)
follows a Brownian motion with u
= 0.01 ando =
0.15.
1. Find the probability that the price has changed by more than 1 dollar after 5 days.
2. Repeat the previous part but for 10 days.
3. Given that the price has increased by exactly 1 dollar in the first 7 days, find the conditional probability that it
will be at least another dollar higher after an additional 7 days.
Transcribed Image Text:Problem 2. Let B(t) represent the change in the price (US dollars) of a barrel of crude oil t days from now. Suppose B(t) follows a Brownian motion with u = 0.01 ando = 0.15. 1. Find the probability that the price has changed by more than 1 dollar after 5 days. 2. Repeat the previous part but for 10 days. 3. Given that the price has increased by exactly 1 dollar in the first 7 days, find the conditional probability that it will be at least another dollar higher after an additional 7 days.
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