Prove integralsare equal byintegrating theirdifferenceL²⊆L¹Prove itfor simpleRVs firstCan't useDCTbecause thesum may notbe L¹π-λtheoremUseenumeration ofℚ or stateseparability as anecessaryconditionPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyConvergencein probabilityWald's1ˢᵗequationWrite ℤ-valued RVas a sum ofindicatorfunctionsThe lim-inf equalsthe limThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁For integersx, y: thenegation ofx≥y is x≤(y-1)Arithmeticwith 0 and ∞to derive acontradictionIdentically distributedRVs have the sameexpectation/varianceStandardize aRV, then use acalculation forthe standardversionWald's2ⁿᵈequationDo somethingwith anonnegative RVthat would notwork for a real-valued RVSomethinglegitimatelyrelevant toVegasA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Probabilitythat 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.Flippanttreatment ofa measure-0setShowintegral is0 usingFatouProve integralsare equal byintegrating theirdifferenceL²⊆L¹Prove itfor simpleRVs firstCan't useDCTbecause thesum may notbe L¹π-λtheoremUseenumeration ofℚ or stateseparability as anecessaryconditionPull sum ofindicatorfunctions out of(or into) anintegral viaBeppo LevyConvergencein probabilityWald's1ˢᵗequationWrite ℤ-valued RVas a sum ofindicatorfunctionsThe lim-inf equalsthe limThe nᵗʰincrement Xₙof a RW isindependentfrom Sₙ₋₁For integersx, y: thenegation ofx≥y is x≤(y-1)Arithmeticwith 0 and ∞to derive acontradictionIdentically distributedRVs have the sameexpectation/varianceStandardize aRV, then use acalculation forthe standardversionWald's2ⁿᵈequationDo somethingwith anonnegative RVthat would notwork for a real-valued RVSomethinglegitimatelyrelevant toVegasA result for allintervals [-∞, b]impliessomethingabout allintervals [a,b]Probabilitythat 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.Flippanttreatment ofa measure-0setShowintegral is0 usingFatou

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.


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