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SOS Final Review - Waterloo SOS STAT 230 Final Review...

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Waterloo SOS Fall 2010 STAT 230 Final Review Package Prepared by Arin Goswami
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STAT 230 Final Review Package Fall 2010 2 Table of Contents Important formulas ............................................................................................................ 3 Chapter 3 - Counting Techniques ....................................................................................... 5 Chapter 4 Probability Rules and Conditional Probability ................................................ 8 Chapter 5 Discrete Distributions .................................................................................... 10 Chapter 7 Expectation, Averages and Variability ........................................................... 17 Chapter 8 Discrete Multivariate Distributions ............................................................... 20 Chapter 9 Continuous Distributions .............................................................................. 30 Extra Practice for Final ...................................................................................................... 37
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STAT 230 Final Review Package Fall 2010 3 Important formulas 1. n (r) = =n(n-1)(n- 2)…(n -r+1) 2. 3. 4. 5. 6. 7. 8. a. b. c. 9. 10. 11. 12.
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STAT 230 Final Review Package Fall 2010 4 13. 14. 15. 16. 17. 18. If X and Y are independent , then Cov(X, Y) = 0 19. The correlation coefficient of X and Y is 20. 21. 22. If we have n identically distributed random variables, and a i = 1 for all I = 1, …, n
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STAT 230 Final Review Package Fall 2010 5 Chapter 3 - Counting Techniques Definitions The Addition Rule : If we can do A in p ways and B in q ways , then we can do either A or B but not both in p + q ways. The Multiplication Rule : If we can do A in p ways and for each of these ways we can do job B in q ways , then we can do both A and B in p x q ways. Permutation Rules : a) The number of ways to arrange n distinct objects in a row is n! = n(n-1)(n- 2)…(1) b) The number of ways to arrange r objects selected from n distinct objects is n (r) = =n(n-1)(n- 2)…(n -r+1) c) The number of distinct arrangements of n objects when n 1 are alike of one type, n 2 alike of a second type, …, n k alike of a k th type (where n 1 + n 2 + … + n k = n) is Combination Rules : The number of ways to choose r objects from n is denoted by The r! in this formula removes the redundant options from the permutations. *Please do not confuse permutations and combinations. Combinations do not keep track of order. Combination is equal to or smaller than its corresponding permutation.
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