FormulaReviewML-21Nov2013 - Supplement for Statistics 260...

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Supplement for Statistics 260 Formula Review 1/5 Flash -Card Formula Review Item Question side of Flash-Card Answer Side of Flash-Card 1 Histograms are used to check the data for outliers, centrality and dispersion. 2 For an observed sample x 1 , x 2 , · · · , x n sample mean x = 1 n n i =1 x i sample median e x = middle ranked observation ( n odd), or average of two middle ranked observations ( n even) sample variance s 2 = 1 n - 1 n i =1 ( x i - x ) 2 sample standard deviation s = s 2 3 B 1 , B 2 , · · · , B n are mutually exclusive iff B i B j = for all i 6 = j 4 P ( B ) = the chance that event B will occur on any trial 5 P ( B 0 ) = P ( B ) = P ( B c ) 1 - P ( B ) 6 P ( A B ) = P ( A ) + P ( B ) - P ( A B ) 7 P ( A B C ) = P ( A ) + P ( B ) + P ( C ) - P ( A B ) - P ( A C ) - P ( B C ) + P ( A B C ) 8 P ( A | B ) = P ( A B ) /P ( B ) 9 P ( A B ) = P ( A ) P ( B | A ) and P ( B ) P ( A | B ) 10 A & B are independent iff P ( A B ) = P ( A ) P ( B ) 11 The cdf of rv X is F ( x ) = P ( X x ) 12 The pmf of discrete rv X is p ( x ) = P ( X = x ) 13 If rv X is discrete, P ( a X b ) = a x b P ( X = x ) 14 If rv X is discrete, E ( X ) = μ x = all x x P ( X = x ) 15 If rv X is discrete, E [ g ( X )] = all x g ( x ) P ( X = x ) 16 V ar ( X ) = σ 2 = σ 2 x = E ( X 2 ) - μ 2 x = E [( X - μ ) 2 ] 17 SD ( X ) = σ = σ x = p V ar ( X )
2/5 18 If X = total number of successes out of n independent trials where P (success)= p on every trial, then the distribution of X is: Binomial ( n, p ) 19 If X Binomial ( n, p ), then formulae for pmf, mean, value, and standard deviation are: n x p x (1 - p ) n - x , np, p np (1 - p ) 20 If events occur at random in time (or space) at the average rate of λ per unit time (or space), and X = total number of events that occur in a time (or space) window of size t , then the distribution of X is: Poisson ( λt ) 21 If X ˜ Poisson( λ ), then formulae for pmf, mean value, and standard deviation are: λ x x ! e - λ , λ, λ 22 If X Binomial ( n, p ), with n large, p small then the distribution of X is well approximated by: Poisson( λ = np ) 23 If rv X is continuous with pdf f, then P ( a X b ) = P ( a < X < b ) = R b a f ( x ) dx 24 If rv X is continuous with pdf f , then E ( X ) = μ x = R x f ( x ) dx 25 If rv X

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