Stat318Midterm 1 Review - 1 • P k,n = n n-1 n-2 n-k 2 n-k...

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Midterm Exam 1 Review You can bring a double-sided cheating sheet and a calculator with you in the exam. The exam will consist of multiple choices and written problems. Please go through all examples discussed in class and the homework problems. Some important concepts and formulas are listed below: Chapter 1: Histogram shape Sample mean, medium, quartiles Range, sample variance, sample standard deviation Chapter 2: Sample space The union, intersection and complement of sets P ( A ) = 1 - P ( A 0 ) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) P ( A B C ) = P ( A )+ P ( B )+ P ( C ) - P ( A B ) - P ( B C ) - P ( A C ) + P ( A B C ) If A 1 , A 2 , A 3 , . . . is an infinite collection of disjoint events, then P ( A 1 A 2 A 3 . . . ) = X i =1 P ( A i ) P ( A ) = N ( A ) N The product rule for ordered pairs and k-tuple
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Unformatted text preview: 1 • P k,n = n ( n-1)( n-2) ... ( n-k + 2)( n-k + 1) C k,n = ( n k ) = n ! k !( n-k )! • P ( A | B ) = P ( A ∩ B ) P ( B ) with P ( B ) > P ( A ∩ B ) = P ( A | B ) · P ( B ) = P ( B | A ) · P ( A ) P ( A 1 ∩ A 2 ∩ A 3 ) = P ( A 3 | A 1 ∩ A 2 ) · P ( A 2 | A 1 ) · P ( A 1 ) • The law of total probability and Bayes’ theorem • Independence: P ( A | B ) = P ( A ) or P ( A ∩ B ) = P ( A ) · P ( B ) or generally P ( A i 1 ∩ A i 2 ∩ ··· ∩ A ik ) = P ( A i 1 ) · P ( A i 2 ) ...P ( A ik ) Exclusive: A ∩ B = ∅ Exhaustive: A ∪ B = S • Venn diagram and tree diagram 2...
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