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# formF02 - FORMULA SHEET STA 2023 x x2(n(x x)2 = s= n1 n1 x...

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STA 2023 FORMULA SHEET Fall, 2002 x = Σ x n s 2 = Σ( x - x ) 2 n - 1 = Σ x 2 - x ) 2 n n - 1 P ( A ) + P ( A c ) = 1 P ( A | B ) = P ( A B ) P ( B ) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) P ( A B ) = P ( A ) P ( B | A ) = P ( B ) P ( A | B ) P ( A ) = P ( A B ) + P ( A B c ) μ = E ( x ) = Σ xp ( x ) σ 2 = E [( x - μ ) 2 ] = Σ( x - μ ) 2 p ( x ) = E ( x 2 ) - μ 2 = Σ x 2 p ( x ) - μ 2 For a binomial random variable: μ = np σ 2 = npq p ( x ) = n x p x q n - x where n x = n ! x !( n - x )! Population Standard Error Estimated or Hypothesized Parameter Estimator of Estimator Standard Error of Estimator μ x σ n s n p ˆ p = x n pq n ˆ p ˆ q n or p o q o n μ 1 - μ 2 x 1 - x 2 σ 2 1 n 1 + σ 2 2 n 2 s 2 1 n 1 + s 2 2 n 2 or s 2 p 1 n 1 + 1 n 2 where s 2 p = ( n 1 - 1) s 2 1 + ( n 2 - 1) s 2 2 n 1 + n 2 - 2 p
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