D 4 points define a decreasing sequence of algebras

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Unformatted text preview: . (5 points) Let and denote: ℱ Find (i) . ℱ Hint. Is the random vector sign sign (ii). 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 are independent, || , and . a. (6 points) Find the density of . Hint: Is symmetric? b. (4 points) Calculate a c. (8 points) Define (i). (ii). (iii). and find the following limits √ ∑ | | ∑ , where | | ∑ . | | . Remark. T...
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