A result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Prove integralsare equal byintegrating theirdifferenceProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)For integersx, y: thenegation ofx≥y is x≤(y-1)Wald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Prove itfor simpleRVs firstDo somethingwith anonnegative RVthat would notwork for a real-valued RVFlippanttreatment ofa measure-0setπ-λtheoremWrite ℤ-valued RVas a sum ofindicatorfunctionsPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyL²⊆L¹Standardize aRV, then use acalculation forthe standardversionCan't useDCTbecause thesum may notbe L¹Convergencein probabilityShowintegral is0 usingFatouThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Useenumeration ofℚ or stateseparability as anecessaryconditionWald's2ⁿᵈequationArithmeticwith 0 and ∞to derive acontradictionSomethinglegitimatelyrelevant toVegasThe lim-inf equalsthe limA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Prove integralsare equal byintegrating theirdifferenceProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)For integersx, y: thenegation ofx≥y is x≤(y-1)Wald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Prove itfor simpleRVs firstDo somethingwith anonnegative RVthat would notwork for a real-valued RVFlippanttreatment ofa measure-0setπ-λtheoremWrite ℤ-valued RVas a sum ofindicatorfunctionsPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyL²⊆L¹Standardize aRV, then use acalculation forthe standardversionCan't useDCTbecause thesum may notbe L¹Convergencein probabilityShowintegral is0 usingFatouThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Useenumeration ofℚ or stateseparability as anecessaryconditionWald's2ⁿᵈequationArithmeticwith 0 and ∞to derive acontradictionSomethinglegitimatelyrelevant toVegasThe lim-inf equalsthe lim

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