Showintegral is0 usingFatouThe lim-inf equalsthe limArithmeticwith 0 and ∞to derive acontradictionA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Write ℤ-valued RVas a sum ofindicatorfunctionsProve itfor simpleRVs firstFor integersx, y: thenegation ofx≥y is x≤(y-1)Convergencein probabilityWald's1ˢᵗequationSomethinglegitimatelyrelevant toVegasProve integralsare equal byintegrating theirdifferenceIdentically distributedRVs have the sameexpectation/varianceDo somethingwith anonnegative RVthat would notwork for a real-valued RVWald's2ⁿᵈequationProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)π-λtheoremThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Can't useDCTbecause thesum may notbe L¹A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFlippanttreatment ofa measure-0setStandardize aRV, then use acalculation forthe standardversionUseenumeration ofℚ or stateseparability as anecessaryconditionL²⊆L¹Showintegral is0 usingFatouThe lim-inf equalsthe limArithmeticwith 0 and ∞to derive acontradictionA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Write ℤ-valued RVas a sum ofindicatorfunctionsProve itfor simpleRVs firstFor integersx, y: thenegation ofx≥y is x≤(y-1)Convergencein probabilityWald's1ˢᵗequationSomethinglegitimatelyrelevant toVegasProve integralsare equal byintegrating theirdifferenceIdentically distributedRVs have the sameexpectation/varianceDo somethingwith anonnegative RVthat would notwork for a real-valued RVWald's2ⁿᵈequationProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)π-λtheoremThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Can't useDCTbecause thesum may notbe L¹A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFlippanttreatment ofa measure-0setStandardize aRV, then use acalculation forthe standardversionUseenumeration ofℚ or stateseparability as anecessaryconditionL²⊆L¹

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