The nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Write ℤ-valued RVas a sum ofindicatorfunctionsConvergencein probabilityπ-λtheoremL²⊆L¹Somethinglegitimatelyrelevant toVegasProve itfor simpleRVs firstCan't useDCTbecause thesum may notbe L¹A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Arithmeticwith 0 and ∞to derive acontradictionProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyDo somethingwith anonnegative RVthat would notwork for a real-valued RVWald's2ⁿᵈequationFor integersx, y: thenegation ofx≥y is x≤(y-1)Identically distributedRVs have the sameexpectation/varianceProve integralsare equal byintegrating theirdifferenceThe lim-inf equalsthe limA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Useenumeration ofℚ or stateseparability as anecessaryconditionShowintegral is0 usingFatouStandardize aRV, then use acalculation forthe standardversionWald's1ˢᵗequationFlippanttreatment ofa measure-0setThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Write ℤ-valued RVas a sum ofindicatorfunctionsConvergencein probabilityπ-λtheoremL²⊆L¹Somethinglegitimatelyrelevant toVegasProve itfor simpleRVs firstCan't useDCTbecause thesum may notbe L¹A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Arithmeticwith 0 and ∞to derive acontradictionProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyDo somethingwith anonnegative RVthat would notwork for a real-valued RVWald's2ⁿᵈequationFor integersx, y: thenegation ofx≥y is x≤(y-1)Identically distributedRVs have the sameexpectation/varianceProve integralsare equal byintegrating theirdifferenceThe lim-inf equalsthe limA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Useenumeration ofℚ or stateseparability as anecessaryconditionShowintegral is0 usingFatouStandardize aRV, then use acalculation forthe standardversionWald's1ˢᵗequationFlippanttreatment ofa measure-0set

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.


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