Flippanttreatment ofa measure-0setThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁For integersx, y: thenegation ofx≥y is x≤(y-1)A result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.L²⊆L¹Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Prove itfor simpleRVs firstArithmeticwith 0 and ∞to derive acontradictionWald's2ⁿᵈequationProve integralsare equal byintegrating theirdifferenceSomethinglegitimatelyrelevant toVegasUseenumeration ofℚ or stateseparability as anecessaryconditionConvergencein probabilityDo somethingwith anonnegative RVthat would notwork for a real-valued RVWrite ℤ-valued RVas a sum ofindicatorfunctionsThe lim-inf equalsthe limWald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceπ-λtheoremStandardize aRV, then use acalculation forthe standardversionCan't useDCTbecause thesum may notbe L¹Showintegral is0 usingFatouFlippanttreatment ofa measure-0setThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁For integersx, y: thenegation ofx≥y is x≤(y-1)A result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.L²⊆L¹Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Prove itfor simpleRVs firstArithmeticwith 0 and ∞to derive acontradictionWald's2ⁿᵈequationProve integralsare equal byintegrating theirdifferenceSomethinglegitimatelyrelevant toVegasUseenumeration ofℚ or stateseparability as anecessaryconditionConvergencein probabilityDo somethingwith anonnegative RVthat would notwork for a real-valued RVWrite ℤ-valued RVas a sum ofindicatorfunctionsThe lim-inf equalsthe limWald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceπ-λtheoremStandardize aRV, then use acalculation forthe standardversionCan't useDCTbecause thesum may notbe L¹Showintegral is0 usingFatou

Math 5530H Bingo 1 - Call List

(Print) Use this randomly generated list as your call list when playing the game. There is no need to say the BINGO column name. Place some kind of mark (like an X, a checkmark, a dot, tally mark, etc) on each cell as you announce it, to keep track. You can also cut out each item, place them in a bag and pull words from the bag.


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
  1. Flippant treatment of a measure-0 set
  2. The nᵗʰ increment Xₙ of a RW is independent from Sₙ₋₁
  3. For integers x, y: the negation of x≥y is x≤(y-1)
  4. A result for all intervals [-∞, b] implies something about all intervals [a,b]
  5. A is the smallest ___ containing B; and C is a ___ containing B; therefore C contains A.
  6. L²⊆L¹
  7. Pull sum of indicator functions out of (or into) an integral via Beppo Levy
  8. Probability that a random walk will exit [a,b] at b is b/(b-a)
  9. Prove it for simple RVs first
  10. Arithmetic with 0 and ∞ to derive a contradiction
  11. Wald's 2ⁿᵈ equation
  12. Prove integrals are equal by integrating their difference
  13. Something legitimately relevant to Vegas
  14. Use enumeration of ℚ or state separability as a necessary condition
  15. Convergence in probability
  16. Do something with a nonnegative RV that would not work for a real-valued RV
  17. Write ℤ-valued RV as a sum of indicator functions
  18. The lim-inf equals the lim
  19. Wald's 1ˢᵗ equation
  20. Identically distributed RVs have the same expectation/variance
  21. π-λ theorem
  22. Standardize a RV, then use a calculation for the standard version
  23. Can't use DCT because the sum may not be L¹
  24. Show integral is 0 using Fatou