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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. ? ?¡ = ?¢??£¤ ¥? ¥¢¦§¥?£¨ ?? ? ©¢??£¤ ¥? ¥¢¦§¥?£¨ ?? ª«?¬­£ ª¬«§£ 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 ²³´µ´²³´²¶ P A ∩ B ¡ = 0 if A and B are ·¸¶¸¹ºº» ´¼½º¸¾¿´ 7. P A À B ¡ = P A ⋂ B ¡ P B ¡ 8. P A ∩ B ¡ = P A ¡ P B À A ¡ P A ∩ B ∩ C ¡ = P A ¡ P B À A ¡ P C À 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, ? Á¡ = ? Á? 1 ¡ + ? Á? 2 ¡ + ⋯ + ? Á? Â ¡ = Ã ? ÁÀ? ? ¡? ( ? ? ) Â ? =1 10. F x ¡ = P X ≤ x ¡ = ® f u ¡ u ≤ x = ® P(X = u) u ≤ x defined for all x ϵℝ 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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Spring 2010 STAT230 midterm1 Package final_merged-1 -...

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