Spring 2010 STAT230 midterm1 Package final_merged-1

Spring 2010 STAT230 midterm1 Package final_merged-1 -...

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Unformatted text preview: Waterloo SOS Spring 2010 STAT 230 Midterm 1 Review Package Prepared by Grace Gu STAT 230 Midterm 1 Review Package Spring 2010 2 Table of Contents Important formulas (Memorizing these should help!) ................................. 3 Chapter 1 Definition of Probability ............................................................ 4 Chapter 2 Mathematical Probability Models ............................................. 5 Chapter 3 - Counting Techniques ................................................................. 6 Chapter 3 - Distinguishing permutations and combinations ..................... 7 Chapter 3 - Counting Technique Examples ................................................ 8 Chapter 4 Probability Rules and Conditional Probability ......................... 13 Chapter 4 Examples ................................................................................ 14 Chapter 5 Discrete Distributions ............................................................. 17 Chapter 5 Examples ................................................................................ 20 Chapters 1 5 Extra Practice ..................................................................... 26 Winter 2010 Midterm 1 with Solutions.32 STAT 230 Midterm 1 Review Package Spring 2010 3 Important formulas (Memorizing these should help!) 1. ? ? = ??? ? ? ?? ? ?? ? ? ?? ? 2. ? ? = ? ( ) A 3. Permutation to arrange r objects from n distinct objects n (r) = n! (n r)! =n(n-1)(n- 2)(n-r+1) 4. Combination to choose r objects from n n (r) r! = n r = n! ! n r ! 5. P A B = P A + P B P(A B) 6. P A B = P A P B if A and B are P A B = 0 if A and B are 7. P A B = P A B P B 8. P A B = P A P B A P A B C = P A P B A P C A B 9. If A 1 , A 2 , , A k is a partition of the sample space into mutually exclusive events, for an arbitrary event B in S, ? = ? ? 1 + ? ? 2 + + ? ? = ? ? ? ? ( ? ? ) ? =1 10. F x = P X x = f u u x = P(X = u) u x defined for all x a. F(x) is a non decreasing function of x. b. F x 1 for all x. c. lim x F x = 0 and lim x F(x) = 1 STAT 230 Midterm 1 Review Package Spring 2010 4 Chapter 1 Definition of Probability Probability is defined in three ways: 1. Classical Definition number of ways the event can occur number of all outcomes in sample space (Provided all points in samples space are equally likely) Limitation E qually likely is a vague term to use but its removal would make the definition unusable in many settings 2. Relative Frequency- The proportion of times the event occurs in a very long series of...
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This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.

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Spring 2010 STAT230 midterm1 Package final_merged-1 -...

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