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formulas201 - MATH201 Formula Sheet n ∑ xi n n 2 2 ∑ xi...

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Unformatted text preview: MATH201 Formula Sheet n ∑ xi n n 2 2 ∑ ( xi − x ) ∑ xi − i =1 n s 2 = i =1 = i =1 n −1 n −1 n x= ∑x i =1 i n QU + 1.5IQR QU + 3IQR QL − 1.5IQR IQR = QU − QL 2 s = s2 p (n + 1) 100 QL − 3IQR z= x−µ σ µ = E ( X ) = ∑ xP( x) σ 2 = ∑ ( x − µ ) 2 P ( x) n n! = x x!(n − x)! µ = np x−x s σ = σ2 n P ( x ) = p x (1 − p ) n − x x z= P( x) = λx e −λ x! µ=λ IQR ≈ 1.3 s x ± zα / 2 x ± zα / 2 σ n n= 2 zα / 2σ 2 E2 σ= λ σx = µx = µ σ n x ± zα / 2 N −n N x ± zα / 2 n= σ = np (1 − p ) σ n x ± tα / 2 s n N −n N 2 zα / 2 p (1 − p ) E2 x ± tα / 2 x−µ σ/ n s ˆ p ± zα / 2 n df = n − 1 n s z= s n df = n − 1 N −n N ˆ p ± zα / 2 ˆ ˆ p (1 − p) n ˆ ˆ p (1 − p ) n ˆ np ≥ 15 ˆ nq ≥ 15 N −n N MATH201 Formula Sheet x − µ0 z= z= σ/ n X2 = t= x − µ0 x − µ0 z= s/ n df = n − 1 s/ n ˆ p − p0 np 0 ≥ 15 p 0 (1 − p 0 ) n nq 0 ≥ 15 (n − 1) s 2 2 σ0 df = n − 1 ( x1 − x 2 ) − D0 z= 2 1 t= ( x1 − x 2 ) − D0 1 1 s + n n 1 2 df = n1 + n 2 − 2 2 p 2 2 s s + n1 n 2 2 (n1 − 1) s12 + (n 2 − 1) s 2 s= n1 + n2 − 2 2 p ( x1 − x 2 ) − D0 t= 2 s12 s 2 + n1 n2 2 ( s12 / n1 + s 2 / n2 ) 2 df = 2 2 ( s1 / n1 ) 2 ( s 2 / n2 ) 2 + n1 − 1 n2 − 1 z= z= ˆ ˆ ( p1 − p 2 ) − D0 1 1 ˆ ˆ p (1 − p ) + n1 n2 ( x1 − x 2 ) ± zα / 2 d ± zα / 2 sd nd 2 s12 s 2 + n1 n2 ˆ p= d − D0 s d / nd t= d − D0 s d / nd 1 1 ( x1 − x 2 ) ± tα / 2 s 2 + p n1 n2 df = n1 + n 2 − 2 sd nd df = n d − 1 sd = df = nd − 1 x1 + x 2 n1 + n 2 d ± tα / 2 nd F= ∑ (d i =1 i − d )2 nd − 1 2 s larger 2 ssmaller ( x1 − x 2 ) ± tα / 2 df = 2 s12 s 2 + n1 n 2 2 ( s12 / n1 + s 2 / n2 ) 2 2 ( s12 / n1 ) 2 ( s 2 / n2 ) 2 + n1 − 1 n2 − 1 ...
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