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HOME ASSIGNMENTS:
- HW 1: hw 1 (pdf file). Assigned August 30,
due September 6.
- HW 2 hw2 (pdf file).
Assigned September 6, due September 13. Question #1 is optional,
extra-credit, 5 extra points out of 60. {Hint: in question 1 the limit
superior is different than the limit inferior (the limit inferior is the
(x,y) such that x2 +y2 < 1, justify and prove that). Note that points
(0,-1) and (0,1) do not belong to limsup and do not belong to liminf.
What is the limit superior?}
- HW 3 hw3 Assigned
9/13/07, due 9/20/07. Exercise #2 in Hw 3 has an extension until 9/27
(it uses the definition of monotone classes that I will introduce on Th.
9/20/07).
- HW 4 hw4 Assigned
9/20 due 9/27. Exercise #5 in HW 4 is optional and extra-credit, 5 extra
points out of 50. In question 3-b there are all equal signs (=).
Question ( c) in 4.11 is not due this week (all the other questions are
due 9/27).
- HW 5 hw5 Assigned 9/27/07 and due 10/4/07.
(please make sure is the lim P(A_n) not the limit of A_n in exercise 3).
- HW 6. hw 6 Assigned 10/4/07 due
10/16/07.
- HW 7. hw7 Assigned 10/25/07, due Nov
1. A normal measure (0,1),
it is your standard normal “probability” measure (the
measure corresponding to the
normal distribution
function).
- HW 8. hw8. Assigned nov 1 (due nov 8).
- HW 9. Hw 9. Assigned nov. 8 due nov 15.
- HW 10. HW 10. Assigned Nov. 15 due Nov. 27.
(read question #5 carefully )
- HW 11 HW 11. Assigned Nov. 27 due Dec. 4
(your last assignment). Hint: for
question 17.11 (a) and (b)
treat upper limit of the integral as a variable and take
derivative with respect to it. (i.e. define F’=f, then F(d)-F(c)= int_c^d f(y)dy. Define G(x)=F(T(x)), then
calculate G’) .For (c) remember that the integral defines a
measure, and the intervals are a pi-system (by extension theorem is
enough).
Note: please the definition of the t
density (updated).
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