Stat 254 Formula Sheet ∑ x i n ∑ (x i - x) 2 n - 1 = ∑ x 2 i - n( x) 2 n - 1 X all x xf (x) Z ∞ -∞ xf (x) dx E (X 2 ) - μ 2 f (x; n, p)= n x p x (1 - p) n-x , E (X )= np, V (X )= np(1 - p) f (x; λ)= e -λ λ x x! , E (X )= λ, V (X )= λ F (x; λ)=1 - e -λx , E (X )=1/λ, V (X )=1/λ 2 X ∼ Gamma(α, β ), E (X )= αβ, V (X )= αβ 2 F (x; α, β )=1 - e -(x/β) α , E (X )= β Γ(1 + 1/α) , V (X )= β 2 Γ(1 + 2/α) - [Γ(1 + 1/α)] 2 Cov (X, Y )= E (XY ) - μ X · μ Y ρ X,Y = Cov (X, Y ) σ X · σ Y 1

254 Formula.pdf0

Download PDF Report

Upload
paba
View
218
Download
4

Embed Size (px)

DESCRIPTION

Stats 254 Formula sheet

Citation preview

Stat254FormulaSheet

xin

(xix)2n 1=

x2i n(x)2n 1

all xxf(x)_xf(x) dx E(X2) 2f(x; n, p) =_nx_px(1 p)nx, E(X) = np, V (X) = np(1 p)f(x; ) =exx!, E(X) = , V (X) = F(x; ) = 1 ex, E(X) = 1/, V (X) = 1/2X Gamma(, ), E(X) = , V (X) = 2F(x; , ) = 1 e(x/), E(X) = (1 + 1/) ,V (X) = 2_(1 + 2/) [(1 + 1/)]2_Cov(X, Y ) = E(XY ) X YX,Y=Cov(X, Y )X Y1Z=X /nx z/2nZ=X S/nx z/2sntn1 =X S/nx t/2,n1snZ= p p_p(1 p)/n p z/2_ p(1 p)ns21n1+s22n2, Z p1(1 p1)n1+ p2(1 p2)n2, Z(n11)s21 + (n21)s22n1 + n22_1n1+1n2_, tn1+n22s21n1+s22n2, t, = integerpartof(s21/n1 + s22/n2)2(s21/n1)2n11+ (s22/n2)2n21estimate (c.v.)(e.s.e.)estimate param.valueunderH0e.s.e.or(s.e.underH0)2