Approximations in Probability Calculations (UMAP)

With completion of this module students will be able to: 1) discuss how approximation is pervasive in statistics; 2) compare structural approximations and mathematical approximations to probability models; 3) describe and recognize a hypergeometric probability distribution and an experiment in which it holds; 4) recognize when hypergeometric probabilites can be approximated adequately by binomial probabilties (or normal or Poisson probabilities); 5) recognize when binomial probabilties can be approximated adequately by normal or Poisson probabilities; 6) recognize when the normal approximation to binomail probabilties requires the continuity correction to be adequate; and 7) calculate hypergeometric or binomial probabilities exactly or approximately.

Table of Contents:

1. INTRODUCTION
1.1 Approximation in Statistics
1.2 Some Examples of Numerical Approximation
1.3 Exercises
1.4 Recursive Formulas
1.5 Exercises

2. STRUCTURAL APPROXIMATION
2.1 Approximation of Hypergeometric Probabilities by Binomial Probabilities
2.2 Exercises

3. MATHEMATICAL APPROXIMATION
3.1 Approximation of Binomial Probabilities Using the Normal Distribution
3.2 Accuracy of the Normal Approximation
3.3 The Continuity Correction to the Normal Approximation
3.4 Approximation of Binomial Probabilites by Poisson Probabilities
3.5 Exercises

4. CONCLUSION
4.1 Summary
4.2 Exercises

5. ANSWERS TO EXERCISES

6. MODEL UNIT EXAM

7. ANSWERS TO MODEL UNIT EXAM