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2 2 n m n m [A]n,m n = m n A At [At]m,n i, j at = aj,i i,j A A = At n = m ai,i n = 1 [A]1,n m = 1 [A]m,1 m, n a at A n | A | n = 2 a1,1 a1,2 = a1,1a2,2 - a1,2a2,1 a1,1 a2,2 n+1 n + 1 n+1 n+1 = (-1)j+1a1,j1,j, n j=1 1,j n n+1 n j [A]n,m, [B]m,l, C = AB. [C]n,l m ci,j = ai,kbk,j, i = 1,..., n, j = 1,...l.

k=1 a n Aa m A, B | AB | = | A | | B |, | At | = | A |.

[I]n,n n [A]n,n AI = IA = A A-1 A AA-1 = A-1A = I.

A a Aa = a a | A - I | = 0.

A(a) = (Aa) = (a), a a n a = a2 j j=1 a n n n n n n m m n A A-1 = At n A a, b < a, b > = arccos, a b < a, b > = akbk k a, b < a, b > = 0.

< a, b > = at b, C = a bt n n ci,j = aibj, i, j = 1,..., n X X x1 xn p1 pn x1,..., xn p1,..., pn F (x) = P (X < t) = pj.

j:xj

k=1 DX = M(X - MX)2.

M(X + Y ) = MX + MY, M(X) = MX, D(X) = 2DX, X, Y MXY = MX MY, D(X + Y ) = DX + DY.

= DX X (MX - 3, MX + 3) X cov(X, Y ) (X, Y ) =, DXDY cov(X, Y ) = MXY - MXMY = M(X - MX)(Y - MY ) X Y X Y (X, Y ) = 0 | (X, Y ) | < 1/3 X Y 1/3 | (X, Y ) | < 2/3 | (X, Y ) | 2/3 > 0 a 2 1 (x - a)2 p(x) = exp -.

22 2 a = 0, = 1 1 (x) = exp(-x2/2).

2 t (t) = (x) dx X a 2 Y = (X - a)/ X - a t - a t - a P (X < t) = P < =.

n x x1,..., xn Mx x C ci,j = cov(xi, xj), i, j = 1,..., n.

cj,j = Dxj C = M(x - Mx)(x - Mx)t.

n n x1 x2 x3, x4, x5 x1, x2 x3, x4, x5 x3 x4, x5 x1 x2 x3 x4 x5 X n n 1 X = xi n i=1 2 n n n 1 1 1 S2 = (xi - X)2 = x2 - xi i n n n i=1 i=1 i=1 x X S2 Mx, Dx S2 n n 1 2 S0 = (xi - X)2.

n - 1 i=1 n n 1 1 AsX = (xi - X)3, ExX = (xi - X)4 - 3.

nS3 nS4 i=1 i=1 S S2 X(1) = min{x1,..., xn}, X(n) = max{x1,..., xn} T = X(n) - X(1).

x1 x2 xk n1 n2 nk k nj = n.

j=k k X = nixi, S2 = ni(xi - X)2, n i=n i=k k AsX = ni(xi - X)3, ExX = ni(xi - X)4 - nS4 i=nSi= k n r = [log2 n] + 1, [.] n r r X(1) - zz1 = X(1) + T/r, zj+1 = zj + T/r, 1 j r - 2, zr = X(n) +.

zr = + j = [zj-1, zj], j = 1,..., r nj j, j = 1,..., r 3 nj 19.

r X x1 x2 xr n1 n2 nr xj j, j = 1,..., r.

xj nj i ni/n, i = 1,..., r (xi, ni/n) n = X(1) X(n) T r = 7 T/r 5, ni i xi ni i i xi ni X = 62, i ni xi xi - X (xi - X) (xi - X) (xi - X) S2 = 55, 90, S = S2 = 7, 48, X max | xi - X | t = S tn t > tn n tn n tn X, S [-, +] 1- - + 1 - 100(1 - ) t t a- = X -, a+ = X +, n n t (-t) =.

t (0, 00) = 0, 500 (-1, 28) = 0, 100 (-1, 64) = 0, (-2, 32) = 0, 010 (-2, 58) = 0, 005 (-2, 98) = 0, (x), x < 0 x (x) = 1 - (-x), x t(x) = e- dt x (x) x (x) SS,n S,n a- = X -, a+ = X +, n - 1 n -,n n-,n n n nS2 nS(2)- =, (2)+ =, + T,n T,n + T,n 2 n - - T,n 1 - 2 n n 10- H0 H X H0 H1 H H HH H H0 HH0 a b a + b H0 e f e + f a + e b + f a H b e a+e b b+f f b+f a a+e a n a e :

a+e e+f e e+f b a+b H H H X Y n, m n m MX = MY n ui = xi - yi, i = 1,..., n, m n 1 X - Y n 2 = ui, SU = (ui - )2, T = n - 1.

n i=n SU i= | T | n - 1 H X Y n = m - MX MY X, Y X, Y n (X, Y ) = 0 X Y R n - T =, 1 - R R n (xi - X)(yi - Y ) n i=R = n (xi - X)2 1 n (yi - Y )n i=1 n i= T n - X n Y m (m - 1)nSX f =, (n - 1)mSY 2 SX, SY X, Y f- f+ n - 1, m - f- f f+ a, 1,..., r p1,..., pr r pi = i= ni, i = 1,..., r r (ni - npi)2 =.

npi i= r - pi i = [zi-1, zi] pi = (zi) - (zi-1).

zi - X zi-1 - X pi = - S S z0 = -, zr = zj zj-X S zj-X (x) S pj npj nj (nj - npj)(nj-npj)npj r - r X = 62, 45, S = 7, 48.

zj - zj-X - S zj-X S pj npj nj (nj - npj)(nj-npj)npj 2 = 6, X n Y m n + m r X n1 nr n Y m1 mr m n1 + m1 nr + mr n + m r r n2 mi i 2 = (n + m) + - n(ni + mi) m(ni + mi) i=1 i= r - X Y X Y 2 = 90(1, 117 - 1) = 10, n 6 di=1 i R(X, Y ) = 1 -.

n3 - n - TX - TY X, Y di i n TX, TY X, Y T = (t3 - tj), j tj j T = R T1 = T2 = T5 = t1 = 2 T3 = (23 - 2)/2 = 3 t1 = 5 T4 = (53 - 5)/2 = 60.

T = ((33 - 3) + (23 - 2))/2 = R(1, 2) = 1 - (1-2)2+(3-1)2+(5-3)2+(7-4)2+(6-7)2+(4-6)2+(2-5) 0, 41.

73-7-0- R(i, j) = R(j, i) R(2, 5) Ti, i = 1, 2, R X Y Y = X +, X = kY + b.

,, k, b n S(, ) = (Yi - Xi - )2 min, i=n T (k, b) = (Xi - kYi - b)2 min k,b i=SY SX Y = (X - X) + Y, X = (Y - Y ) + X, SX SY SX, SY X, Y X Y X r A1,..., Ar Y s B1,..., Bs i,j Ai Bj X, Y i,j X Ai Y Bj n1,..., nr X A1,..., Ar m1,..., ms Y B1,..., Bs Y(i) = Yk, i = 1,..., r, ni {k:XkAi} X(j) = Xk, j = 1,..., s.

mj {k:YkBj} (Xi, Y(i)), i = 1,..., r (X(j), Yj), j = 1,..., s Xi Ai Yj Bj Y X X Y X D0X X X D D0X DX > D0X, DX = D0X + DAX, DAX DX = D0X + DAX + DBX + DA,BX +...

X X m n X i j xi,j A1 Am x1,1 x1,m n xn,1 xn,m x1 xm N = nm m n m 1 X = xj = xi,j.

m nm j=1 i=1 j=m n m n m (xi,j - X)2 = (xi,j - xj)2 + n (xj - X)2.

j=1 i=1 j=1 i=1 j= Q Q0 n QA Q X Q QA X m n m n Q = x2 - xi,j ;

j=1 i=1 i,j j=1 i=N m n m n Q0 = x2 - ( xi,j)2 ;

j=1 i=1 i,j j=1 i=n m n m n 1 QA = ( xi,j)2 - xi,j.

n j=1 i=1 N j=1 i=QA Q0 nDA + DDA =, D0 =, F =.

N - 1 N - 1 D F m-1, m(n-1) A X N z = (S1 + S2 + S3)/15 = 7539, 0.

t QA = z - = 89, 2, DA = 2, N Sj t u Sj v Q0 = u - z = 262, 0, D0 = 5, t Q = u - = 351, N F = 6, QA Q n p p q q p p x(1),...x(p) X = (x(1),..., x(p)), Z = Z(X) q q p Z(X) = (Z(1)(X),..., Z(q)(X)) Iq(Z(X)) I F Z Z F Iq(Z(X)) = max Iq(Z(X)).

ZF I, F F p Z(j) = cj,k(x(k) - x(k)), j = 1,..., q, k=p p c2 = 1, j = 1,..., q, cj,kci,k = 0, j, k = 1,.., q, j = k.

j.k k=1 k=q DZ(j) j=Iq(Z) =.

p Dx(j) j= x(1),..., x(p) S1,..., Sq Z F DZ = q Iq(Z, S) = 2(x(k), Z(j)), j=1 kSj (.,.) S i,j di,j n n (Z) = d | di,j(Z) - di,j |.

i,j i=1 j= di,j, < Iq(Z) =.

1 + (Z) F 1 q Z(X) = (Xi ),..., X(i )).

k Iq(Z) = (Pi(Z), Pj(Z)), i,j= k (.,.) (Pi(Z), Pj(Z)) = (Xi - Xj)2.

Y aX +b X p S pp q Dz(j) j=Iq = max, p Dx(i) i= Z = L(X - ), L - q p X k k- L (1) lj x(j) max, (1) (1) Si,jli lj max, (1) i,j (lj )2 = 1, < Sl(1), l(1) > max, l1 = 1, l l(j) j S j j S Iq =, 1 +... + p x1 x2 x 451, 39 271, 17 168, S = 271, 17 171, 73 103, 29.

168, 70 103, 29 66, 1 = 680, 40, 2 = 6, 50 3 = 2, 86.

0, 81 -0, 55 -0, l1 = 0, 50, l2 = 0, 83, l3 = -0, 25.

0, 31 0, 10 0. i z(i) = < li, X > X xj Z = 0, 9864, 1 + 2 + x(1),..., x(p) f(1),..., f(q) f f(i) x(j) X = QF + U, Q - p q F X U U F V U X X = AF, Df(i) = 1, i = 1, 2...

A F Z = CF, X = (AC)Z C A, F F (m) m Am X X(m) = AmF (m).

X X(m) f(i) = f(i), i f(i) i i A ili li S i x(i), x(j) x(i), x(j) q1,1 0 0... q2,1 q2,2 0..................

Q =, qq,1 qq,2 qq,3... qq,q...............

qp,1 qp,2 qp,3... qp,q Q V x(1),..., x(p) i j i,j Dx(i) f(1) f(1) x(i1) = x(i) - qi,1f(1).

Q V V = S - QQt.

Q, V F q x q (j) x(i) = qi,jfk + u(i), i = 1,..., p, k = 1,..., n.

k k j=- Fk = (QtV Q)-1QtXk, k = 1,..., n.

ci,j F = CX n q p (i) M(fk - ci,jx(k))2 min.

j C k=1 i=1 j=(i) fk t X X QQt + V Q M =.

F F Qt I -1 - Fk = (I + QtV Q)-1QV Xk, k = 1,..., n.

x1 x2 x3 x4 x5 x6 qi,1 qi,xxxxxxf1 = 0, 245x1 + 0, 208x2 + 0, 158x3 + 0, 278x4 + 0, 271x5 + 0, 157x6, f2 = 0, 352x1 + 0, 201x2 + 0, 309x3 - 0, 351x4 - 0, 303x5 - 0, 126x6.

f1 fl l i,j i j l p q q < p l i j i,j = 1 - i,j, i,j q x0 i = 1,...p, k = 1,..., q i,k, i,j d0 = (x0 - xi,k j,k)2.

k i,j i,j = i,j, d (i,j - di,j)i,j S =.

i,j di,j (i, j), i, j = 1,..., p i,j di,j c+i,j xc+1 = xc - i,k j,k) i,k i,k p j 1 - (xc - xc dc i,j i,j dc+1 = (xc+1 - xc+1)2, i,k j,k k c+ i,j c S c+ i,j i,j dc+ X n p x lx c(x), j = 1,..., lx j n n c(x) = 0; (c(x) )2 = 1, r(i) r(i) n i=1 i= r(i) x i Q = 2, i,j i

Qx3 x4 x




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