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Unformatted text preview: . (5 points) Let
and denote: ℱ
Hint. Is the random vector sign
d. ℱ | . (4 points) Define a decreasing sequence of σ-algebras, ℱ , so that
) ℱ } is a backwards martingale. || independent of ℱ | Problem 5 (18 pts). Let
be independent and identically distributed
random variables. We assume that
, where a
|| , and . a. (6 points)
Find the density of .
Hint: Is symmetric?
b. (4 points)
Calculate a c. (8 points)
(iii). and find the following limits √ ∑ | | ∑ , where
| ∑ .
| | . Remark. T...
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- Spring '12