Ответы на задачи типового расчета по теме:

Непрерывные случайные величины

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Случайные величины |Содержание | Условия

ЗАДАЧА N 1

1. F(x)=1/2(1-cos(8x)), H=4, P=0.1012, M= 1.767, D= 0.007, Mx=0.0855;
2. F(x)=exp(2x)/3.00, H=0.67, P=0.2505, M= 0.051, D= 0.248, Mx=0.4983;
3. F(x)=1/2(sin(x/6+1), H=1/12, P=0.4852, M= 75.398, D=16.826, Mx=4.1020;
4. F(x)=exp(5x)/0.04, H=128.95, P=0.0189, M= -0.850, D= 0.762, Mx=0.8732;
5. F(x)=1/2(1-cos(4x)), H=2, P=0.0927, M= 3.534, D= 0.029, Mx=0.1709;
6. F(x)=1/2(sin(2x)+1), H=1, P=0.0397, M= -9.425, D= 0.117, Mx=0.3418;
7. F(x)=exp(2x)/0.90-0.01,H=2.22, P=0.1270, M= -0.537, D= 0.503, Mx=0.7090;
8. F(x)=1/2(sin(x/3+1), H=1/ 6, P=0.0577, M= 37.699, D= 4.207, Mx=2.0510;
9. F(x)=exp(3x)/0.11, H=28.47, P=0.0573, M= -1.083, D= 1.283, Mx=1.1325;
10. F(x)=1/2(sin(x/7+1), H=1/14, P=0.0069, M= 87.965, D=22.903, Mx=4.7857;
11. F(x)=1/2(1-cos(2x)), H=1, P=0.3792, M= -5.498, D= 0.117, Mx=0.3418;
12. F(x)=1/2(sin(x/2+1), H=1/ 4, P=0.3209, M= 12.566, D= 1.870, Mx=1.3673;
13. F(x)=exp(2x)/0.74, H=2.70, P=0.6319, M= -0.647, D= 0.658, Mx=0.8113;
14. F(x)=1/2(sin(x/8+1), H=1/16, P=0.2259, M= 50.265, D=29.914, Mx=5.4693;
15. F(x)=1/2(1-cos(7x)), H=3.5, P=0.0850, M= 2.917, D= 0.010, Mx=0.0977;
16. F(x)=1/2(sin(x/2+1), H=1/ 4, P=0.5068, M= 25.133, D= 1.870, Mx=1.3673;
17. F(x)=1/2(sin(5x)+1), H=2.5, P=0.1010, M= -3.770, D= 0.019, Mx=0.1367;
18. F(x)=1/2(sin(x/3+1), H=1/ 6, P=0.0064, M= 18.850, D= 4.207, Mx=2.0510;
19. F(x)=exp(x)/0.83-0.04,H=1.21, P=0.3364, M= -1.019, D= 1.595, Mx=1.2629;
20. F(x)=0.042x**3-0.11, H=0.042, P=0.2657, M= 3.418, D=12.067, Mx= 3.474;
21. F(x)=1/2(1-cos(x/8), H=1/16, P=0.0015, M= 113.097, D=29.914, Mx=5.4693;
22. F(x)=1/2(1-cos(x/7), H=1/14, P=0.0024, M= 54.978, D=22.903, Mx=4.7857;
23. F(x)=1/2(sin(2x)+1), H=1, P=0.6011, M= 12.566, D= 0.117, Mx=0.3418;
24. F(x)=1/2(1-cos(7x)), H=3.5, P=0.2905, M= -3.366, D= 0.010, Mx=0.0977;
25. F(x)=1/2(sin(7x)+1), H=3.5, P=0.5212, M= 1.795, D= 0.010, Mx=0.0977;
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ЗАДАЧА N 2

1. p(y)=[((y-6)/6)]/[П(1+((y-6)/6)**(2)];
2. p(y)=[exp(((y-9)/19)**2 /2)/(2П**(1/2))]*[((y-9)/19)]
3. p(y)=[(0.26(y-12)/19)**(4/5)]/[П(1+((y-12)/19)**(2/5))];
4. p(y)=[(0.83(y-7)/6)**(4/5)]/[П(1+((y-7)/6)**(2/5))];
5. p(y)=[exp(((y-18)/20)**2 /2)/(2П**(1/2))]*[((y-18)/20)]
6. p(y)=[exp(((y-10)/17)**2 /2)/(2П**(1/2))]*[(0.18(y-10)/17)**(2/3)]
7. p(y)=[exp(((y-16)/19)**2 /2)/(2П**(1/2))]*[(0.16(y-16)/19)**(2/3)]
8. p(y)=[exp(((y-20)/7)**2 /2)/(2П**(1/2))]*[(0.43(y-20)/7)**(2/3)]
9. p(y)=[exp(((y-9)/12)**2 /2)/(2П**(1/2))]*[(0.42(y-9)/12)**(4/5)]
10. p(y)=[((y-17)/13)]/[П(1+((y-17)/13)**(2)];
11. p(y)=[((y-10)/21)]/[П(1+((y-10)/21)**(2)];
12. p(y)=[exp(((y-9)/12)**2 /2)/(2П**(1/2))]*[(0.42(y-9)/12)**(4/5)]
13. p(y)=[exp(((y-16)/4)**2 /2)/(2П**(1/2))]*[(1.25(y-16)/4)**(4/5)]
14. p(y)=[((y-16)/6)]/[П(1+((y-16)/6)**(2)];
15. p(y)=[(0.33(y-8)/9)**(2/3)]/[П(1+((y-8)/9)**(2/3))];
16. p(y)=[((y-14)/17)]/[П(1+((y-14)/17)**(2)];
17. p(y)=[(0.20(y-13)/15)**(2/3)]/[П(1+((y-13)/15)**(2/3))];
18. p(y)=[exp(((y-5)/14)**2 /2)/(2П**(1/2))]*[((y-5)/14)]
19. p(y)=[exp(((y-13)/8)**2 /2)/(2П**(1/2))]*[(0.63(y-13)/8)**(4/5)]
20. p(y)=[exp(((y-21)/16)**2 /2)/(2П**(1/2))]*[((y-21)/16)]
21. p(y)=[exp(((y-6)/20)**2 /2)/(2П**(1/2))]*[(0.25(y-6)/20)**(4/5)]
22. p(y)=[(0.38(y-2)/13)**(4/5)]/[П(1+((y-2)/13)**(2/5))];
23. p(y)=[exp(((y-4)/9)**2 /2)/(2П**(1/2))]*[(0.56(y-4)/9)**(4/5)]
24. p(y)=[exp(((y-14)/19)**2 /2)/(2П**(1/2))]*[(0.16(y-14)/19)**(2/3)]
25. p(y)=[exp(((y-7)/3)**2 /2)/(2П**(1/2))]*[(1.00(y-7)/3)**(2/3)]
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ЗАДАЧА N 3

1.а) P=0.2008,б) P=0.8414,в) P=0.2811; 2.а) P=0.1361,б) P=0.7570,в) P=0.5565;
3.а) P=0.1869,б) P=0.8697,в) P=0.6685; 4.а) P=0.1606,б) P=0.7769,в) P=0.0296;
5.а) P=0.1076,б) P=0.3640,в) P=0.1501; 6.а) P=0.0808,б) P=0.1647,в) P=0.0543;
7.а) P=0.2220,б) P=0.9233,в) P=0.5528; 8.а) P=0.3515,б) P=0.4995,в) P=0.5566;
9.а) P=0.2232,б) P=0.6204,в) P=0.0611;10.а) P=0.3656,б) P=0.4038,в) P=0.2603;
11.а) P=0.1144,б) P=0.3613,в) P=0.4753;12.а) P=0.1204,б) P=0.9523,в) P=0.1131;
13.а) P=0.0325,б) P=0.8963,в) P=0.4063;14.а) P=0.1486,б) P=0.7565,в) P=0.6140;
15.а) P=0.1277,б) P=0.9706,в) P=0.2259;16.а) P=0.1267,б) P=0.7534,в) P=0.0545;
17.а) P=0.1441,б) P=0.9835,в) P=0.8037;18.а) P=0.1593,б) P=0.9182,в) P=0.6068;
19.а) P=0.2113,б) P=0.9695,в) P=0.7531;20.а) P=0.3678,б) P=0.3323,в) P=0.4888;
21.а) P=0.1666,б) P=0.9553,в) P=0.7293;22.а) P=0.3365,б) P=0.3476,в) P=0.3871;
23.а) P=0.1316,б) P=0.5987,в) P=0.5284;24.а) P=0.1953,б) P=0.8178,в) P=0.5842;
25.а) P=0.0885,б) P=0.2778,в) P=0.2992;
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ЗАДАЧА N 4

1. P=0.173; 2. P=0.117; 3. P=0.344; 4. P=0.222; 5. P=0.576;
6. P=0.504; 7. P=0.000; 8. P=0.341; 9. P=0.048; 10. P=0.115;
11. P=0.038; 12. P=0.196; 13. P=0.552; 14. P=0.262; 15. P=0.656;
16. P=0.132; 17. P=0.017; 18. P=0.159; 19. P=0.233; 20. P=0.500;
21. P=0.250; 22. P=0.394; 23. P=0.038; 24. P=0.423; 25. P=0.000;
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ЗАДАЧА N 5

Вариант 1.

а) X: -1 0 1 | Y: -1 0 1
P{X=Xi}: 0.197 0.582 0.221 |P{Y=Yi}:0.253 0.533 0.214
б) Зависимы.
в) P{X>Y}=0.241.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y
X\|_______|_________|_________|_______

x<=-1 | 0 0 0 0
-1<x<= 0| 0 0.071 0.138 0.197
0<x<= 1| 0 0.162 0.637 0.779
1 < x | 0 0.253 0.786 1.000

M[X]=0.024, M[Y]=-0.040;
д) K[X,Y]=-0.006, R[X,Y]=-0.013;
е) X(i): -1 0 1
P{X=x(i)/Y= 3}: 0.125 0.765 0.110
M[X/Y= 3]=-0.015.

Вариант 2.

а) X: 0 1 2 | Y: 1 2 3 4
P{X=Xi}: 0.274 0.472 0.254 |P{Y=Yi}:0.167 0.427 0.163 0.244
б) Зависимы.
в) P{X>Y}=0.050.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y
X\|_______|_________|_________|_________|_______

x<= 0 | 0 0 0 0 0
0<x<= 1| 0 0.071 0.119 0.190 0.274
1<x<= 2| 0 0.117 0.461 0.580 0.746
2 < x | 0 0.167 0.594 0.756 1.000

M[X]=0.980, M[Y]=2.483;
д) K[X,Y]=-0.010, R[X,Y]=-0.013;
е) X(i): 0 1 2
P{X=x(i)/Y= 4}: 0.342 0.342 0.316
M[X/Y= 4]=0.974.

Вариант 3.

а) X: -2 -1 0 1 | Y: -1 0 1 2
P{X=Xi}: 0.168 0.493 0.166 0.174 |P{Y=Yi}:0.179 0.508 0.144 0.170
б) Зависимы.
в) P{X>Y}=0.144.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_________|_________|_______

x<=-2 | 0 0 0 0 0
-2<x<=-1| 0 0.050 0.095 0.128 0.168
-1<x<= 0| 0 0.090 0.497 0.573 0.660
0<x<= 1| 0 0.133 0.586 0.695 0.826
1 < x | 0 0.179 0.687 0.830 1.000

M[X]=-0.654, M[Y]=0.304;
д) K[X,Y]=0.041, R[X,Y]=0.046;
е) X(i): -2 -1 0 1
P{X=x(i)/Y= 3}: 0.225 0.303 0.232 0.240
M[X/Y= 3]=-0.512.

Вариант 4.

а) X: -2 -1 0 | Y: 0 1 2 3
P{X=Xi}: 0.227 0.538 0.234 |P{Y=Yi}:0.153 0.493 0.144 0.211
б) Зависимы.
в) P{X>Y}=0.000.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|_______

x<=-2 | 0 0 0 0 0
-2<x<=-1| 0 0.050 0.113 0.156 0.227
-1<x<= 0| 0 0.100 0.521 0.617 0.766
0 < x | 0 0.153 0.645 0.789 1.000

M[X]=-0.993, M[Y]=1.413;
д) K[X,Y]=-0.019, R[X,Y]=-0.029;
е) X(i): -2 -1 0
P{X=x(i)/Y= 4}: 0.127 0.728 0.145
M[X/Y= 4]=-0.982.

Вариант 5.

а) X: 0 1 2 3 | Y: 1 2 3 4 5
P{X=Xi}: 0.206 0.470 0.151 0.173 |P{Y=Yi}:0.155 0.421 0.135 0.155 0.135
б) Зависимы.
в) P{X>Y}=0.101.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y<= 5 | 5<y
X\|_______|_________|_________|_________|_________|_______

x<= 0 | 0 0 0 0 0 0
0<x<= 1| 0 0.050 0.095 0.130 0.180 0.206
1<x<= 2| 0 0.081 0.443 0.512 0.602 0.676
2<x<= 3| 0 0.107 0.500 0.605 0.723 0.827
3 < x | 0 0.155 0.576 0.711 0.865 1.000

M[X]=1.291, M[Y]=2.694;
д) K[X,Y]=0.087, R[X,Y]=0.069;
е) X(i): 0 1 2 3
P{X=x(i)/Y= 1}: 0.324 0.202 0.166 0.308
M[X/Y= 1]=1.459.

Вариант 6.

а) X: 1 2 3 4 | Y: 0 1 2
P{X=Xi}: 0.180 0.451 0.195 0.174 |P{Y=Yi}:0.230 0.486 0.284
б) Зависимы.
в) P{X>Y}=0.79
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_________|_______

x<= 1 | 0 0 0 0
1<x<= 2| 0 0.050 0.109 0.180
2<x<= 3| 0 0.109 0.483 0.631
3<x<= 4| 0 0.168 0.601 0.826
4 < x | 0 0.230 0.716 1.000

M[X]=2.362, M[Y]=1.054;
д) K[X,Y]=-0.030, R[X,Y]=-0.044;
е) X(i): 1 2 3 4
P{X=x(i)/Y= 2}: 0.251 0.271 0.271 0.207
M[X/Y= 2]=2.433.

Вариант 7.

а) X: -1 0 1 2 3 | Y: 1 2 3
P{X=Xi}: 0.139 0.398 0.153 0.159 0.151 |P{Y=Yi}:0.241 0.541 0.219
б) Зависимы.
в) P{X>Y}=0.158.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_______

x<=-1 | 0 0 0 0
-1<x<= 0| 0 0.045 0.084 0.139
0<x<= 1| 0 0.091 0.447 0.538
1<x<= 2| 0 0.150 0.561 0.691
2<x<= 3| 0 0.202 0.676 0.849
3 < x | 0 0.241 0.781 1.000

M[X]=0.782, M[Y]=1.978;
д) K[X,Y]=-0.010, R[X,Y]=-0.012;
е) X(i): -1 0 1 2 3
P{X=x(i)/Y= 3}: 0.254 0.163 0.176 0.199 0.208
M[X/Y= 3]=0.943.

Вариант 8.

а) X: -1 0 1 | Y: 0 1 2
P{X=Xi}: 0.225 0.515 0.259 |P{Y=Yi}:0.270 0.486 0.244
б) Зависимы.
в) P{X>Y}=0.111.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_________|_______

x<=-1 | 0 0 0 0
-1<x<= 0| 0 0.100 0.159 0.225
0<x<= 1| 0 0.159 0.574 0.741
1 < x | 0 0.270 0.756 1.000

M[X]=0.034, M[Y]=0.974;
д) K[X,Y]=0.000, R[X,Y]=0.000;
е) X(i): -1 0 1
P{X=x(i)/Y= 2}: 0.274 0.411 0.316
M[X/Y= 2]=0.042.

Вариант 9.

а) X: 1 2 3 4 5 | Y: -1 0
P{X=Xi}: 0.139 0.407 0.146 0.177 0.130 |P{Y=Yi}:0.357 0.643
б) Зависимы.
в) P{X>Y}=1.000.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y
X\|_______|_________|_______

x<= 1 | 0 0 0
1<x<= 2| 0 0.083 0.139
2<x<= 3| 0 0.142 0.546
3<x<= 4| 0 0.198 0.693
4<x<= 5| 0 0.298 0.870
5 < x | 0 0.357 1.000

M[X]=2.752, M[Y]=-0.357;
д) K[X,Y]=-0.081, R[X,Y]=-0.133;
е) X(i): 1 2 3 4 5
P{X=x(i)/Y= 1}: 0.323 0.258 0.179 0.239 3725040223600000000.000
M[X/Y= 1]=18625201118000000000.000.

Вариант 10.

а) X: -1 0 | Y: -2 -1
P{X=Xi}: 0.393 0.607 |P{Y=Yi}:0.393 0.607
б) Зависимы.
в) P{X>Y}=0.857.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y
X\|_______|_________|______

x<=-1 | 0 0 0
-1<x<= 0| 0 0.250 0.393
0 < x | 0 0.393 1.000
M[X]=-0.393, M[Y]=-1.393;
д) K[X,Y]=0.096, R[X,Y]=0.401;
е) X(i): -1 0
P{X=x(i)/Y= 1}: 0.636 0.364
M[X/Y= 1]=-0.636.

Вариант 11.

а) X: 0 1 2 | Y: -1 0
P{X=Xi}: 0.333 0.417 0.250 |P{Y=Yi}:0.383 0.617
б) Зависимы.
в) P{X>Y}=0.833.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y
X\|_______|_________|_______

x<= 0 | 0 0 0
0<x<= 1| 0 0.167 0.333
1<x<= 2| 0 0.258 0.750
2 < x | 0 0.383 1.000

M[X]=0.917, M[Y]=-0.383;
д) K[X,Y]=0.010, R[X,Y]=0.027;
е) X(i): 0 1 2
P{X=x(i)/Y= 1}: 0.270 0.528 0.202
M[X/Y= 1]=0.933.

Вариант 12.

а) X: -1 0 | Y: -2 -1 0 1 2
P{X=Xi}: 0.395 0.605 |P{Y=Yi}:0.177 0.406 0.191 0.114 0.111
б) Зависимы.
в) P{X>Y}=0.500.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_________|_________|_________|_________

x<=-1 | 0 0 0 0 0 0
-1<x<= 0| 0 0.100 0.183 0.283 0.342 0.395
0 < x | 0 0.177 0.583 0.774 0.889 1.000

M[X]=-0.395, M[Y]=-0.423;
д) K[X,Y]=-0.048, R[X,Y]=-0.080;
е) X(i): -1 0
P{X=x(i)/Y= 4}: 0.565 0.435
M[X/Y= 4]=-0.565.

Вариант 13.

а) X: 1 2 | Y: 1 2 3 4 5
P{X=Xi}: 0.389 0.611 |P{Y=Yi}:0.155 0.417 0.119 0.153 0.156
б) Зависимы.
в) P{X>Y}=0.071.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y<= 5 | 5<y
X\|_______|_________|_________|_________|_________|_________

x<= 1 | 0 0 0 0 0 0
1<x<= 2| 0 0.083 0.174 0.227 0.289 0.389
2 < x | 0 0.155 0.572 0.691 0.844 1.000

M[X]=1.611, M[Y]=2.738;
д) K[X,Y]=-0.107, R[X,Y]=-0.166;
е) X(i): 1 2
P{X=x(i)/Y= 5}: 0.643 0.357
M[X/Y= 5]=1.357.

Вариант 14.

а) X: -2 -1 | Y: -2 -1 0
P{X=Xi}: 0.307 0.693 |P{Y=Yi}:0.236 0.548 0.216
б) Зависимы.
в) P{X>Y}=0.111.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y
X\|_______|_________|_________|_______

x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.125 0.216 0.307
-1 < x | 0 0.236 0.784 1.000

M[X]=-1.307, M[Y]=-1.020;
д) K[X,Y]=0.028, R[X,Y]=0.090;
е) X(i): -2 -1
P{X=x(i)/Y= 2}: 0.529 0.471
M[X/Y= 2]=-1.529.

Вариант 15.

а) X: -2 -1 0 | Y: 0 1 2 3
P{X=Xi}: 0.197 0.553 0.250 |P{Y=Yi}:0.160 0.494 0.165 0.182
б) Зависимы.
в) P{X>Y}=0.000.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|______

x<=-2 | 0 0 0 0 0
-2<x<=-1| 0 0.045 0.101 0.154 0.197
-1<x<= 0| 0 0.093 0.520 0.640 0.750
0 < x | 0 0.160 0.654 0.818 1.000

M[X]=-0.947, M[Y]=1.368;
д) K[X,Y]=0.008, R[X,Y]=0.012;
е) X(i): -2 -1 0
P{X=x(i)/Y= 2}: 0.319 0.405 0.276
M[X/Y= 2]=-1.044.

Вариант 16.

а) X: -1 0 1 | Y: -1 0 1 2 3
P{X=Xi}: 0.199 0.575 0.226 |P{Y=Yi}:0.122 0.479 0.141 0.148 0.110
б) Зависимы.
в) P{X>Y}=0.134.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|_________|________

x<=-1 | 0 0 0 0 0 0
-1<x<= 0| 0 0.040 0.088 0.126 0.163 0.199
0<x<= 1| 0 0.082 0.508 0.606 0.698 0.774
1 < x | 0 0.122 0.601 0.742 0.890 1.000

M[X]=0.027, M[Y]=0.646;
д) K[X,Y]=0.021, R[X,Y]=0.027;
е) X(i): -1 0 1
P{X=x(i)/Y= 1}: 0.273 0.418 0.309
M[X/Y= 1]=0.036.

Вариант 17.

а) X: 0 1 2 | Y: 1 2 3
P{X=Xi}: 0.216 0.549 0.234 |P{Y=Yi}:0.268 0.512 0.221
б) Зависимы.
в) P{X>Y}=0.091.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|________

x<= 0 | 0 0 0 0
0<x<= 1| 0 0.077 0.139 0.216
1<x<= 2| 0 0.177 0.612 0.766
2 < x | 0 0.268 0.779 1.000

M[X]=1.018, M[Y]=1.953;
д) K[X,Y]=-0.023, R[X,Y]=-0.050;
е) X(i): 0 1 2
P{X=x(i)/Y= 1}: 0.287 0.373 0.339
M[X/Y= 1]=1.052.

Вариант 18.

а) X: 0 1 2 3 | Y: 1 2
P{X=Xi}: 0.171 0.528 0.138 0.162 |P{Y=Yi}:0.300 0.700
б) Зависимы.
в) P{X>Y}=0.229.
г)
\Y| y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_______

x<= 0 | 0 0 0
0<x<= 1| 0 0.071 0.171
1<x<= 2| 0 0.162 0.700
2<x<= 3| 0 0.229 0.838
3 < x | 0 0.300 1.000

M[X]=1.291, M[Y]=1.700;
д) K[X,Y]=-0.051, R[X,Y]=-0.118;
е) X(i): 0 1 2 3
P{X=x(i)/Y= 1}: 0.238 0.303 0.222 0.238
M[X/Y= 1]=1.460.

Вариант 19.

а) X: -1 0 1 2 3 | Y: 0 1 2
P{X=Xi}: 0.148 0.360 0.158 0.177 0.158 |P{Y=Yi}:0.285 0.449 0.266
б) Зависимы.
в) P{X>Y}=0.335.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y
X\|_______|_________|_________|_______

x<=-1 | 0 0 0 0
-1<x<= 0| 0 0.063 0.103 0.148
0<x<= 1| 0 0.097 0.400 0.507
1<x<= 2| 0 0.156 0.502 0.665
2<x<= 3| 0 0.218 0.620 0.842
3 < x | 0 0.285 0.734 1.000

M[X]=0.837, M[Y]=0.981;
д) K[X,Y]=-0.047, R[X,Y]=-0.048;
е) X(i): -1 0 1 2 3
P{X=x(i)/Y= 2}: 0.171 0.235 0.209 0.221 0.164
M[X/Y= 2]=0.971.

Вариант 20.

а) X: 0 1 2 | Y: -1 0 1 2 3
P{X=Xi}: 0.252 0.514 0.234 |P{Y=Yi}:0.118 0.423 0.155 0.146 0.158
б) Зависимы.
в) P{X>Y}=0.535.
г)
\Y| y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|_________|_______

x<= 0 | 0 0 0 0 0 0
0<x<= 1| 0 0.034 0.097 0.134 0.190 0.252
1<x<= 2| 0 0.080 0.451 0.550 0.656 0.766
2 < x | 0 0.118 0.542 0.697 0.842 1.000

M[X]=0.982, M[Y]=0.801;
д) K[X,Y]=-0.047, R[X,Y]=-0.053;
е) X(i): 0 1 2
P{X=x(i)/Y= 5}: 0.148 0.728 0.124
M[X/Y= 5]=0.977.

Вариант 21.

а) X: -2 -1 0 1 | Y: -2 -1 0 1
P{X=Xi}: 0.168 0.487 0.179 0.166 |P{Y=Yi}:0.175 0.485 0.172 0.169
б) Зависимы.
в) P{X>Y}=0.252.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y
X\|_______|_________|_________|_________|_______

x<=-2 | 0 0 0 0 0
-2<x<=-1| 0 0.053 0.090 0.131 0.168
-1<x<= 0| 0 0.091 0.480 0.555 0.655
0<x<= 1| 0 0.135 0.564 0.701 0.834
1 < x | 0 0.175 0.659 0.831 1.000

M[X]=-0.658, M[Y]=-0.665;
д) K[X,Y]=0.040, R[X,Y]=0.044;
е) X(i): -2 -1 0 1
P{X=x(i)/Y= 1}: 0.220 0.371 0.198 0.212
M[X/Y= 1]=-0.598.

Вариант 22.

а) X: 1 2 3 4 5 | Y: -2 -1 0 1
P{X=Xi}: 0.141 0.468 0.128 0.138 0.124 |P{Y=Yi}:0.164 0.511 0.175 0.150
б) Зависимы.
в) P{X>Y}=0.967.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y
X\|_______|_________|_________|_________|_______

x<= 1 | 0 0 0 0 0
1<x<= 2| 0 0.028 0.068 0.108 0.141
2<x<= 3| 0 0.053 0.466 0.540 0.609
3<x<= 4| 0 0.087 0.531 0.642 0.737
4<x<= 5| 0 0.124 0.608 0.755 0.876
5 < x | 0 0.164 0.675 0.850 1.000

M[X]=2.636, M[Y]=-0.688;
д) K[X,Y]=0.019, R[X,Y]=0.016;
е) X(i): 1 2 3 4 5
P{X=x(i)/Y= 4}: 0.222 0.237 0.175 0.170 0.196
M[X/Y= 4]=2.881.

Вариант 23.

а) X: 1 2 | Y: 0 1 2 3
P{X=Xi}: 0.431 0.569 |P{Y=Yi}:0.222 0.306 0.222 0.250
б) Зависимы.
в) P{X>Y}=0.444.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|_______

x<= 1 | 0 0 0 0 0
1<x<= 2| 0 0.111 0.194 0.306 0.431
2 < x | 0 0.222 0.528 0.750 1.000

M[X]=1.569, M[Y]=1.500;
д) K[X,Y]=-0.035, R[X,Y]=-0.064;
е) X(i): 1 2
P{X=x(i)/Y= 4}: 0.500 0.500
M[X/Y= 4]=1.500.

Вариант 24.

а) X: -1 0 1 2 3 | Y: -2 -1
P{X=Xi}: 0.174 0.412 0.146 0.142 0.125 |P{Y=Yi}:0.347 0.653
б) Зависимы.
в) P{X>Y}=0.909.
г)
\Y| y<=-2 |-2<y<=-1 |-1<y
X\|_______|_________|______

x<=-1 | 0 0 0
-1<x<= 0| 0 0.083 0.174
0<x<= 1| 0 0.146 0.587
1<x<= 2| 0 0.229 0.732
2<x<= 3| 0 0.288 0.875
3 < x | 0 0.347 1.000

M[X]=0.632, M[Y]=-1.347;
д) K[X,Y]=-0.075, R[X,Y]=-0.124;
е) X(i): -1 0 1 2 3
P{X=x(i)/Y= 1}: 0.500 0.500 0.105 0.103 0.118
M[X/Y= 1]=0.163.

Вариант 25.

а) X: 1 2 | Y: 0 1 2 3
P{X=Xi}: 0.379 0.621 |P{Y=Yi}:0.183 0.410 0.225 0.183
б) Зависимы.
в) P{X>Y}=0.481.
г)
\Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
X\|_______|_________|_________|_________|_______

x<= 1 | 0 0 0 0 0
1<x<= 2| 0 0.071 0.183 0.308 0.379
2 < x | 0 0.183 0.592 0.817 1.000

M[X]=1.621, M[Y]=1.408;
д) K[X,Y]=-0.042, R[X,Y]=-0.088;
е) X(i): 1 2
P{X=x(i)/Y= 4}: 0.391 0.609
M[X/Y= 4]=1.609.