A-exam Prep

1234567891011121314151617181920212223242526272829303132333435
Across
  1. 3. If you take the ratio of two N(0,1) random variables, you will get this distribution
  2. 4. Jensen's inequality states that g(E[x]) <= E[g(x)] if g(.) is ___
  3. 10. For Q to be a pivot, its ___ cannot depend on theta
  4. 12. In the A/R algorithm, M is the expected number of ___
  5. 13. This theorem is useful when dealing with convergence in distribution as well as convergence in probability to a constant
  6. 14. Gamma(1/2) is the square root of this constant
  7. 17. This number of conditions must be satisfied for something to be a valid probability function
  8. 18. Any one-to-one function of a minimal sufficient statistic will be ___
  9. 21. This lemma gives us a recipe for constructing a level alpha UMP test
  10. 22. We can actually minimize Bayes Risk by minimizing this thing (which is easier)
  11. 23. -2log(lambda), where lambda is the LRT statistic, follows this distribution asymptotically
  12. 24. Is an algebra always a sigma algebra?
  13. 26. If we let Y equal the cdf of X, then Y follows this distribution
  14. 28. These things from regression should always sum to zero
  15. 29. A chi-squared distribution is a special case of this distribution
  16. 30. This is the strongest form of convergence that we learned about
  17. 31. E[Y|X] is a ___ (first two words: function of)
  18. 32. For an estimator to be UMVUE, its variance has to attain this (hint: acronym)
  19. 33. When the first derivative is 0, which order of delta method should you use?
  20. 34. The mgf of a t distribution ___
  21. 35. When finding the kth factorial moment from a pgf, you should differentiate the pgf k times and evaluate it at s = ___
Down
  1. 1. An ancillary statistic is independent of a minimal sufficient statistic if this minimal statistic is also ___
  2. 2. This theorem is very helpful for showing minimal sufficiency
  3. 5. The mgf of this distribution, evaluated at n, can be used to find the nth moment of the lognormal distribution
  4. 6. When finding P(X=k) from a pgf, you should multiply (1/k!) by the kth derivative of the pgf and evaluate it at s = ___
  5. 7. A sigma algebra should always contain this set
  6. 8. If the ratio of p(x|theta)/q(T(x)|theta) is constant with respect to theta, then T(x) is ___
  7. 9. f(y|x) is a ___ (first two words: function of)
  8. 11. This is what allows you to easily find the MLE of a function of an MLE
  9. 15. Under suitable regularity conditions, MLE's are asymptotically these two things
  10. 16. A prediction interval is ___ than a corresponding confidence interval
  11. 19. We can use this algorithm to generate two independent N(0,1) RV's
  12. 20. For a level alpha test, the probability of a type I error is always ___ alpha
  13. 25. For E[S^2] to equal sigma^2, we require that the x_i's be ___
  14. 27. One thing that the geometric and exponential distributions have in common is that both are ___