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# b.home - partitioning a large compact interval into short...

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Probability II MAP6473 4810 Home-B Prof. JLF King 4May2010 Please. General instructions/notation are on the Checklist . Please type every 2nd or 3rd line. ( Don’t Scrunch! ) Exam is due by 1PM, Friday, 23Apr2004 . B1: For a prob.meas. μ , let ˜ μ be μ “flipped”; so ˜ μ ( B ) := μ ( - B ). Write the char.fnc ϕ ˜ μ ITOf ( In Terms Of ) ϕ μ . Let h μ ; 7 i and h μ ; 7 , 3 i be a translation and a translation-scaling of μ : h μ ; 7 i ( B ) := μ ( B - 7) ; h μ ; 7 , 3 i ( B ) := μ (3 B - 7) . Describe the char.fncs ϕ h μ ;7 i and ϕ h μ ;7 , 3 i ITOf ϕ μ . B2: Please do Billingley: 26.1 P.353. Use A,B for a,b . The “lattice” is L := A + B Z , a scaled translation of the integers. For each integer n , there is a mass m n := P ( X = A + Bn ); they sum to 1. B3: Billingley: 26.2 P.353. B4: Billingley: 26.5 P.354. B5: Bill: 26.15 P.355. Remember the tool of partitioning a large compact interval into short
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Unformatted text preview: partitioning a large compact interval into short subintervals, where all the separation points are continuity-points of μ . B6: Bill: 24.6 P.326. As it was stated in class, the pointwise Ergodic Theorem applies to L 1-fncs. B1: 70pts B2: 70pts B3: 70pts B4: 70pts B5: 70pts B6: 70pts Total: 420pts Please PRINT your name and student ordinal ; Ta: .............................................. Ord: Honor Code: “I have neither requested nor re-ceived help on this exam other than from my professor (or his colleague) .” Signature: .........................................
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