Standardize aRV, then use acalculation forthe standardversionSomethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctionsPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFlippanttreatment ofa measure-0setThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Probabilitythat arandom walkwill exit [a,b]at b is b/(b-a)A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.L²⊆L¹The lim-inf equalsthe limArithmeticwith 0 and ∞to derive acontradictionCan't useDCTbecause thesum may notbe L¹A result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]π-λtheoremShowintegral is0 usingFatouDo somethingwith anonnegative RVthat would notwork for a real-valued RVConvergencein probabilityWald's2ⁿᵈequationIdentically distributedRVs have the sameexpectation/varianceWald's1ˢᵗequationProve integralsare equal byintegrating theirdifferenceUseenumeration ofℚ or stateseparability as anecessaryconditionFor integersx, y: thenegation ofx≥y is x≤(y-1)Prove itfor simpleRVs firstStandardize aRV, then use acalculation forthe standardversionSomethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctionsPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFlippanttreatment ofa measure-0setThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Probabilitythat arandom walkwill exit [a,b]at b is b/(b-a)A is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.L²⊆L¹The lim-inf equalsthe limArithmeticwith 0 and ∞to derive acontradictionCan't useDCTbecause thesum may notbe L¹A result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]π-λtheoremShowintegral is0 usingFatouDo somethingwith anonnegative RVthat would notwork for a real-valued RVConvergencein probabilityWald's2ⁿᵈequationIdentically distributedRVs have the sameexpectation/varianceWald's1ˢᵗequationProve integralsare equal byintegrating theirdifferenceUseenumeration ofℚ or stateseparability as anecessaryconditionFor integersx, y: thenegation ofx≥y is x≤(y-1)Prove itfor simpleRVs first

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