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Flashcards

A8

Ben Tidswell Part A uni English 37 cards

A8

Cards in this deck (37)

  1. 1State the Weak Law of Large NumbersState the Weak Law of Large Numbers
  2. 2State and prove Markov's inequalityState and prove Markov's inequality
  3. 3State and prove Chebyshev's inequalityState and prove Chebyshev's inequality
  4. 4State the Strong Law of Large NumbersState the Strong Law of Large Numbers
  5. 5State the Central Limit TheoremState the Central Limit Theorem
  6. 6State the Uniqueness theorem for probability generating functionsState the Uniqueness theorem for probability generating functions
  7. 7State the Convergence theorem for probability generating functionsState the Convergence theorem for probability generating functions
  8. 8State and prove Chapman-KolmogorovState and prove Chapman-Kolmogorov
  9. 9State the Existence and uniqueness of stationary distributionsState the Existence and uniqueness of stationary distributions
  10. 10State the Convergence to equilibrium of stationary distributionsState the Convergence to equilibrium of stationary distributions
  11. 11State the Ergodic theoremState the Ergodic theorem
  12. 12State the Superposition of Poisson processesState the Superposition of Poisson processes
  13. 13State the Thinning of a Poisson processState the Thinning of a Poisson process
  14. 14State the pdf of a Gamma(alpha,beta) distributionState the pdf of a Gamma(alpha,beta) distribution
  15. 15State the mean and variance of an Exp(lambda) distributionState the mean and variance of an Exp(lambda) distribution
  16. 16State the formula for cov(X,Y)State the formula for cov(X,Y)
  17. 17Define a communicating classDefine a communicating class
  18. 18Define hitting probabilitiesDefine hitting probabilities
  19. 19Define the moment generating function for a r.v. XDefine the moment generating function for a r.v. X
  20. 20Define a Poisson process via Poisson distribution of incrementsDefine a Poisson process via Poisson distribution of increments
  21. 21State the p.m.f. of a Poisson(lambda) distributionState the p.m.f. of a Poisson(lambda) distribution
  22. 22State and prove the weak law of large numbers in the case of random variables with finite varianceState and prove the weak law of large numbers in the case of random variables with finite variance
  23. 23Define a transition matrixDefine a transition matrix
  24. 24State the Markov propertyState the Markov property
  25. 25State the period of a state i∈IState the period of a state i∈I
  26. 26Let λ be the initial distribution. Prove that the distribution of X_n is λP^nLet λ be the initial distribution. Prove that the distribution of X_n is λP^n
  27. 27Give another name for an invariant distribution and give an iff condition for a diistribution to be invariantGive another name for an invariant distribution and give an iff condition for a diistribution to be invariant
  28. 28State the change of variables for bivariate probability density functionsState the change of variables for bivariate probability density functions
  29. 29State the kth derivative of M_X(t) at t=0State the kth derivative of M_X(t) at t=0
  30. 30State the p.d.f. of a N(μ,σ^2) distributionState the p.d.f. of a N(μ,σ^2) distribution
  31. 31State the expansion of log(1+x)State the expansion of log(1+x)
  32. 32Define convergence in probabilityDefine convergence in probability
  33. 33State what it means for a transition matrix P to be irreducibleState what it means for a transition matrix P to be irreducible
  34. 34State what it means for π to be a stationary distributionState what it means for π to be a stationary distribution
  35. 35Define almost sure convergenceDefine almost sure convergence
  36. 36Define convergence in distributionDefine convergence in distribution
  37. 37State the continuity theorem for mgfsState the continuity theorem for mgfs

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uni Part A Flashcards on A8, created by Ben Tidswell on 31/03/2022.
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Ben Tidswell
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