| 16.1
| Х
|
|
|
|
| У
| 0,2
| 0,8
|
|
| p
| 0,26
| 0,38
| 0,36
|
| p
| 0,56
| 0,44
|
| Х у = 0,2
|
|
|
|
| У х = 3
| 0,2
| 0,8
|
| p
| 0,321
| 0,393
| 0,286
|
| p
| 0,579
| 0,421
|
16.2. M[Х]=0,69; M[X2]=0,867; D[Х]=0,3909, s [Х]=0,6252; M[У]=1,5; M[Y2] = 2,5; D[Y]=0,25, s [Y]=0,5; M[XY]=1,07; Kxy = 0,035; r xy =0,11196; 16.3. M[Х]=1,4; M[X2]=2,38; D[Х]=0,42, s [Х]=0,648; M[У]=0,6; M[Y2]=0,78; D[Y]=0,42, s [Y]=0,648; M[XY]=0,42;
Kxy = –0,42; rxy = –1; зависимы;
16.4. f(x) = 2(1 – x) при 0 £ x £ 1; M[Х]= 
; M[X2] = 
; D[Х] = 
, s [Х] = 
; f(y) = 2(1 – y) при 0 £ y £ 1; M[У]= ; M[Y2]= ; D[Y]= 
, s [Y] = 
; M[XY]= 
; Kxy = – 
; rxy = – 
; F(x;y) = 2(1 – x)(1 – y) при (х;у) Î D; 16.5. а = 4; f(x) = 2 x при x Î[0;1], f(y) = 2 y при y Î[0;1]; f(xy) = 4 xy = 2 x 2 y = f(x)f(y) Þ X и Y независимы Þ Kxy = rxy = 0, f(yx) = 2 y, y Î[0;1], f(xy) = 2 x, x Î[0;1]; 16.6. f(x) = 
,
x Î[–5;5]; M[Х]=0; s [Х]=2,5; f(y) = 
, yÎ[–5;5]; M[Y]=0, s [Y]=2,5; M[XY]=0; Kxy = rxy =0; f(x)f(y) = 
= f(x; y) Þ X и Y – зависимы; 16.7. f(xy) = 
; 16.8. M[Х]=0,17; M[X2]=0,079; D[Х]=0,0501, s [Х]=0,2238; M[У]=1,45; M[Y2]=2,275; D[Y]=0,1725, s [Y]=0,4153; M[XY] = 0,28; Kxy =0,0335; rxy = 0,3604; yx = 0,6687 x + 1,3363; xy =0,1942 y – 0,1116; 16.9. M[Х]=0,5; M[X2]=0,4; D[Х]=0,15, s [Х]=0,3873; M[У]=0,75; M[Y2] = 0,625; D[Y]=0,0625, s [Y]=0,25; M[XY]=0,375; Kxy =0; 16.10. f(x) = 2 x, x Î[0;1], f(y) = 0,5 y, y Î[0;1], f(xy) = xy = 2 x ×0,5 y = f(x)f(y) Þ X и Y независимы Þ Kxy = rxy =0, f(x;y) = 0,25 x 2 y 2, (x;y) Î D; 16.11. fx(x) = 0,5(sinx + cosx), x Î 
, fy(y) =0,5(siny + cosy), y Î , M[Х]=M[Y]= 
; M[X2]= =M[Y2]= 
; D[X]=D[Y]= 
; s [X]= s [Y]»0,4332; M[XY]= 
; Kxy = 
»0,0461; rxy»–0,2455; x и y – зависимы; 
, (x,y) Î D; 
, (x,y) ÎD;
16.12. f(x,y) = ab е – (ах+bх) ; 16.13. M[Х]=1,4; M[X2] = 2,15; D[Х]=0,19, s [Х]=0,4359; M[У]=0,7; M[Y2]=1,1; D[Y]=0,61, s [Y]=0,7810; M[XY]=1; Kxy = 0,02; r xy =0,0587; yx =0,1053 x + 0,5526; xy = 0,0328 y + 1,3770 (или y = 30,5 x –42).
