test2formsheet515spr11

test2formsheet515spr11 - Formula Sheet – Test 2 – STAT...

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Unformatted text preview: Formula Sheet – Test 2 – STAT 515 For X ∼ Poisson(λ): P (x) = λx e−λ x! For X ∼ Uniform(c,d): P (a < X < b) = Z= b−a c+d d−c , µ= , σ= √ d−c 2 12 X −µ , X = Zσ + µ σ ¯ X −µ √ σ/ n Z= √ x ± tα/2 (s/ n), ¯ where tα/2 based on n − 1 df p(1 − p) ˆ ˆ n p ± zα/2 ˆ (n − 1)s2 (n − 1)s2 , χ2 2 χ2−α/2 α/ 1 s2 /s2 12 s2 /s2 12 , Fα/2(n1 −1,n2 −1) 1/Fα/2(n2 −1,n1 −1) Sample size formulas: n= (zα/2 )2 σ 2 (zα/2 )2 pq , n= B2 B2 Test statistic: t= x − µ0 ¯ √ s/ n 1 ...
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