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Exam 1 - Crib Sheet

# Exam 1 - Crib Sheet - Crib Sheet for Exam#1 Statistics 211...

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Crib Sheet for Exam #1 Statistics 211 1 Chapter 1: Descriptive Statistics Sample Average Population Average ¯ x = 1 n n i =1 x i μ = 1 N N i =1 x i To caluclate the p ’th percentile x [ p ] : 1. Let x ( i ) refer to our data set in ascending order. 2. Let i p = np/ 100. 3. Find the first index i such that i > i p . 4. The p ’th percentile is then: x [ p ] = braceleftbigg x ( i - 1) + x ( i ) 2 if i - 1 = i p x ( i ) otherwise s 2 = 1 n - 1 summationdisplay ( x i - ¯ x ) 2 = 1 n - 1 parenleftBig summationdisplay x 2 i - (∑ x i ) 2 n parenrightBig Chebychev’s Rule: The proportion of observations that are within k standard deviations ( p k ) of the mean is at least: p k = 1 - 1 k 2 2 Chapter 2: Probability Multiplication rule Permutation Combination n 1 × n 2 × n 2 ... × n k P k,n = n ! ( n - k )! ( n k ) = P k,n k ! = n ! k !( n - k )! For any two events A and B : P ( A B ) = P ( A ) + P ( B ) - P ( A B ) The conditional probability of A given that B occurred ( P ( B ) > 0): P ( A | B ) = P ( A B ) P ( B ) Two events A and B are independent if P ( A | B ) = P ( A ) If A and B are independent then P ( A B ) = P ( A ) P ( B ) If A,B,C,D,... are mutually independent then P ( A B C D... ) = P ( A ) P ( B ) P ( C ) P ( D ) ...

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