π-λtheoremA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Do somethingwith anonnegative RVthat would notwork for a real-valued RVL²⊆L¹Wald's2ⁿᵈequationWald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceUseenumeration ofℚ or stateseparability as anecessaryconditionThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Flippanttreatment ofa measure-0setA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Showintegral is0 usingFatouConvergencein probabilityCan't useDCTbecause thesum may notbe L¹Prove itfor simpleRVs firstThe lim-inf equalsthe limStandardize aRV, then use acalculation forthe standardversionPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFor integersx, y: thenegation ofx≥y is x≤(y-1)Arithmeticwith 0 and ∞to derive acontradictionProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Prove integralsare equal byintegrating theirdifferenceSomethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctionsπ-λtheoremA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Do somethingwith anonnegative RVthat would notwork for a real-valued RVL²⊆L¹Wald's2ⁿᵈequationWald's1ˢᵗequationIdentically distributedRVs have the sameexpectation/varianceUseenumeration ofℚ or stateseparability as anecessaryconditionThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Flippanttreatment ofa measure-0setA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Showintegral is0 usingFatouConvergencein probabilityCan't useDCTbecause thesum may notbe L¹Prove itfor simpleRVs firstThe lim-inf equalsthe limStandardize aRV, then use acalculation forthe standardversionPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyFor integersx, y: thenegation ofx≥y is x≤(y-1)Arithmeticwith 0 and ∞to derive acontradictionProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Prove integralsare equal byintegrating theirdifferenceSomethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctions

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