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Exam 2: Wednesday, November 14 (take home will be handed out on November 7 at the end of class).

Final: Take home that will be handed out on last day of class and will be due by 10AM, December 18.

Let X(t) = N(t) - t, where N(t) is the usual Poisson process. Show that X(t) and X(t)^2 - t are martingales relative to the filtration associated to N(t).

Using the Ito calculus, find d[exp(B_t)]; find d[sin(B_t)]; and d[exp(t B_t)].

Do Problems 1, 2, 4 of 12.1 and Problem 1 of 12.4.

Do the problems on the Sample test.

Do Problems 1, 2, 3, 9, 12 of 6.1; and Problem 2 of 6.2.

Do Problems 16, 17 of 1.8; Problems 2 (skip the variance question), 8a, 9 of 5.1; Problems 1, 2a of 5.3; and Problems 1a, 2 of 5.10.

Do Problem 8 of 3.6; Problem 4 of 3.7; Problems 5b, 13a of 3.11; and Problems 1, 2 (assume the pdf f is continuous) of 4.2.

Do Problem 4, 6, 7, 19 of 2.7; Problem 1 of 3.1; Problem 4a of 3.2; and Problem 6 of 3.3.

Do Problem 2 (with n = 3) of 1.5; Problem 22, 34 of 1.8.

Do Problem 2, 4 of 1.2; Problems 5 of 1.3; Problem 3 of 1.4; Problem 9 of 1.5.

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