Showintegral is0 usingFatouProve itfor simpleRVs firstA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Somethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctionsπ-λtheoremL²⊆L¹Standardize aRV, then use acalculation forthe standardversionDo somethingwith anonnegative RVthat would notwork for a real-valued RVProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Wald's2ⁿᵈequationIdentically distributedRVs have the sameexpectation/varianceThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Flippanttreatment ofa measure-0setArithmeticwith 0 and ∞to derive acontradictionFor integersx, y: thenegation ofx≥y is x≤(y-1)Useenumeration ofℚ or stateseparability as anecessaryconditionProve integralsare equal byintegrating theirdifferenceWald's1ˢᵗequationConvergencein probabilityCan't useDCTbecause thesum may notbe L¹The lim-inf equalsthe limPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Showintegral is0 usingFatouProve itfor simpleRVs firstA is the smallest___ containing B;and C is a ___containing B;therefore Ccontains A.Somethinglegitimatelyrelevant toVegasWrite ℤ-valued RVas a sum ofindicatorfunctionsπ-λtheoremL²⊆L¹Standardize aRV, then use acalculation forthe standardversionDo somethingwith anonnegative RVthat would notwork for a real-valued RVProbabilitythat arandom walkwill exit [a,b]at b is b/(b-a)Wald's2ⁿᵈequationIdentically distributedRVs have the sameexpectation/varianceThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁Flippanttreatment ofa measure-0setArithmeticwith 0 and ∞to derive acontradictionFor integersx, y: thenegation ofx≥y is x≤(y-1)Useenumeration ofℚ or stateseparability as anecessaryconditionProve integralsare equal byintegrating theirdifferenceWald's1ˢᵗequationConvergencein probabilityCan't useDCTbecause thesum may notbe L¹The lim-inf equalsthe limPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]

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