Prove integralsare equal byintegrating theirdifferenceConvergencein probabilityThe lim-inf equalsthe limWald's2ⁿᵈequationShowintegral is0 usingFatouProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Somethinglegitimatelyrelevant toVegasA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyCan't useDCTbecause thesum may notbe L¹Useenumeration ofℚ or stateseparability as anecessaryconditionArithmeticwith 0 and ∞to derive acontradictionProve itfor simpleRVs firstπ-λtheoremFor integersx, y: thenegation ofx≥y is x≤(y-1)A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Flippanttreatment ofa measure-0setIdentically distributedRVs have the sameexpectation/varianceWrite ℤ-valued RVas a sum ofindicatorfunctionsDo somethingwith anonnegative RVthat would notwork for a real-valued RVStandardize aRV, then use acalculation forthe standardversionL²⊆L¹The nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Wald's1ˢᵗequationProve integralsare equal byintegrating theirdifferenceConvergencein probabilityThe lim-inf equalsthe limWald's2ⁿᵈequationShowintegral is0 usingFatouProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Somethinglegitimatelyrelevant toVegasA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Pull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyCan't useDCTbecause thesum may notbe L¹Useenumeration ofℚ or stateseparability as anecessaryconditionArithmeticwith 0 and ∞to derive acontradictionProve itfor simpleRVs firstπ-λtheoremFor integersx, y: thenegation ofx≥y is x≤(y-1)A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Flippanttreatment ofa measure-0setIdentically distributedRVs have the sameexpectation/varianceWrite ℤ-valued RVas a sum ofindicatorfunctionsDo somethingwith anonnegative RVthat would notwork for a real-valued RVStandardize aRV, then use acalculation forthe standardversionL²⊆L¹The nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Wald's1ˢᵗequation

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