Ответы на задачи типового расчета по теме
Случайные векторы
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ЗАДАЧА
Вариант 1.
а) X: -2 -1 0 | Y: 1 2 3
P{X=Xi}: 0.225 0.578 0.196 |P{Y=Yi}:0.193 0.578 0.229
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y
_____ X_\|________|__________|__________|__________
x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.059 0.142 0.225
-1<x<= 0| 0 0.121 0.637 0.804
0 < x | 0 0.193 0.771 1.000
M[X]=-1.029, M[Y]=2.036;
д) K[X,Y]=-0.032, R[X,Y]=-0.077;
е) X(i): -2 -1 0
P{X=x(i)/Y= 2}: 0.144 0.748 0.108
M[X/Y= 2]=-1.036.
Вариант 2.
а) X: -2 -1 | Y: 0 1 2 3 4
P{X=Xi}: 0.325 0.675 |P{Y=Yi}:0.155 0.371 0.155 0.153 0.167
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 |
3<y<= 4 | 4<y_____ X_\|________|__________|__________|__________|__________|__________
x<=-2 | 0 0 0 0 0 0
-2<x<=-1| 0 0.071 0.134 0.205 0.258 0.325
-1 < x | 0 0.155 0.526 0.681 0.833 1.000
M[X]=-1.325, M[Y]=1.805;
д) K[X,Y]=-0.044, R[X,Y]=-0.070;
е) X(i): -2 -1
P{X=x(i)/Y= 3}: 0.345 0.655
M[X/Y= 3]=-1.345.
Вариант 3.
а) X: 0 1 2 3
| Y: -2 -1 0P{X=Xi}: 0.157 0.479 0.175 0.189 |P{Y=Yi}:0.201 0.554 0.245
б) Зависимы.
в) P{X>Y}=0.947.
г) \Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y
_____ X_\|________|__________|__________|__________
x<= 0 | 0 0 0 0
0<x<= 1| 0 0.045 0.104 0.157
1<x<= 2| 0 0.112 0.530 0.636
2<x<= 3| 0 0.158 0.629 0.811
3 < x | 0 0.201 0.755 1.000
M[X]=1.397, M[Y]=-0.956;
д) K[X,Y]=0.045, R[X,Y]=0.070;
е) X(i): 0 1 2 3
P{X=x(i)/Y= 1}: 0.215 0.215 0.314 0.255
M[X/Y= 1]=1.610.
Вариант 4.
а) X: 0 1 | Y: 0 1
P{X=Xi}: 0.400 0.600 |P{Y=Yi}:0.450 0.550
б) Зависимы.
в) P{X>Y}=0.250.
г) \Y| y<= 0 | 0<y<= 1 | 1<y
_____ X_\|________|__________|__________
x<= 0 | 0 0 0
0<x<= 1| 0 0.200 0.400
1 < x | 0 0.450 1.000
M[X]=0.600, M[Y]=0.550;
д) K[X,Y]=0.020, R[X,Y]=0.082;
е) X(i): 0 1
P{X=x(i)/Y= 2}: 0.444 0.556
M[X/Y= 2]=0.556.
Вариант 5.
а) X: 0 1 2 | Y: 1 2 3 4 5
P{X=Xi}: 0.211 0.565 0.224 |P{Y=Yi}:0.114 0.482 0.116 0.142 0.147
б) Зависимы.
в) P{X>Y}=0.034.
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 0.043 0.081 0.122 0.161 0.211
1<x<= 2| 0 0.079 0.522 0.601 0.687 0.776
2 < x | 0 0.114 0.595 0.711 0.853 1.000
M[X]=1.014, M[Y]=2.727;
д) K[X,Y]=0.055, R[X,Y]=0.066;
е) X(i): 0 1 2
P{X=x(i)/Y= 5}: 0.339 0.261 0.399
M[X/Y= 5]=1.060.
Вариант 6.
а) X: -1 0 | Y: 1 2
P{X=Xi}: 0.417 0.583 |P{Y=Yi}:0.417 0.583
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 1 | 1<y<= 2 | 2<y
_____ X_\|________|__________|__________
x<=-1 | 0 0 0
-1<x<= 0| 0 0.250 0.417
0 < x | 0 0.417 1.000
M[X]=-0.417, M[Y]=1.583;
д) K[X,Y]=0.076, R[X,Y]=0.314;
е) X(i): -1 0
P{X=x(i)/Y= 1}: 0.600 0.400
M[X/Y= 1]=-0.600.
Вариант 7.
а) X: 1 2 3 | Y: -2 -1
P{X=Xi}: 0.267 0.465 0.268 |P{Y=Yi}:0.410 0.590
б) Зависимы.
в) P{X>Y}=1.000.
г) \Y| y<=-2 |-2<y<=-1 |-1<y
_____ X_\|________|__________|__________
x<= 1 | 0 0 0
1<x<= 2| 0 0.100 0.267
2<x<= 3| 0 0.267 0.732
3 < x | 0 0.410 1.000
M[X]=2.001, M[Y]=-1.410;
д) K[X,Y]=-0.042, R[X,Y]=-0.118;
е) X(i): 1 2 3
P{X=x(i)/Y= 2}: 0.282 0.506 0.212
M[X/Y= 2]=1.929.
Вариант 8.
а) X: -2 -1 0 1
2 | Y: 1 2 3 4P{X=Xi}: 0.141 0.451 0.142 0.143 0.122 |P{Y=Yi}:0.171 0.476 0.198 0.154
б) Зависимы.
в) P{X>Y}=0.029.
г) \Y| y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y
_____ X_\|________|__________|__________|__________|__________
x<=-2 | 0 0 0 0 0
-2<x<=-1| 0 0.026 0.056 0.101 0.141
-1<x<= 0| 0 0.052 0.429 0.524 0.592
0<x<= 1| 0 0.092 0.505 0.632 0.735
1<x<= 2| 0 0.142 0.585 0.750 0.878
2 < x | 0 0.171 0.648 0.846 1.000
M[X]=-0.346, M[Y]=2.335;
д) K[X,Y]=-0.011, R[X,Y]=-0.009;
е) X(i): -2 -1 0 1 2
P{X=x(i)/Y= 3}: 0.229 0.252 0.163 0.187 0.168
M[X/Y= 3]=-0.188.
Вариант 9.
а) X: -2 -1 0 | Y: -2 -1 0
P{X=Xi}: 0.234 0.516 0.250 |P{Y=Yi}:0.241 0.527 0.232
б) Зависимы.
в) P{X>Y}=0.233.
г) \Y|
y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y_____ X_\|________|__________|__________|__________
x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.091 0.158 0.234
-1<x<= 0| 0 0.158 0.602 0.750
0 < x | 0 0.241 0.768 1.000
M[X]=-0.984, M[Y]=-1.009;
д) K[X,Y]=0.014, R[X,Y]=0.030;
е) X(i): -2 -1 0
P{X=x(i)/Y= 2}: 0.126 0.716 0.158
M[X/Y= 2]=-0.968.
Вариант 10.
а) X: 1 2 |
Y: 0 1 2 3 4P{X=Xi}: 0.380 0.620 |P{Y=Yi}:0.162 0.422 0.105 0.127 0.183
б) Зависимы.
в) P{X>Y}=0.484.
г) \Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y
_____ X_\|________|__________|__________|__________|__________|__________
x<= 1 | 0 0 0 0 0 0
1<x<= 2| 0 0.071 0.171 0.224 0.280 0.380
2 < x | 0 0.162 0.584 0.690 0.817 1.000
M[X]=1.620, M[Y]=1.747;
д) K[X,Y]=-0.109, R[X,Y]=-0.164;
е) X(i): 1 2
P{X=x(i)/Y= 2}: 0.500 0.500
M[X/Y= 2]=1.500.
Вариант 11.
а) X: -2 -1 0 | Y: -2 -1 0
P{X=Xi}: 0.250 0.516 0.234 |P{Y=Yi}:0.277 0.466 0.258
б) Зависимы.
в) P{X>Y}=0.244.
г) \Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y
_____ X_\|________|__________|__________|__________
x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.100 0.183 0.250
-1<x<= 0| 0 0.200 0.599 0.766
0 < x | 0 0.277 0.742 1.000
M[X]=-1.016, M[Y]=-1.019;
д) K[X,Y]=0.047, R[X,Y]=0.092;
е) X(i): -2 -1 0
P{X=x(i)/Y= 2}: 0.179 0.678 0.143
M[X/Y= 2]=-1.036.
Вариант 12.
а) X: -1 0 | Y: 1 2 3 4 5
P{X=Xi}: 0.405 0.595 |P{Y=Yi}:0.127 0.440 0.127 0.182 0.124
б) Зависимы.
в) P{X>Y}=0.000.
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<= 0| 0 0.071 0.171 0.243 0.334 0.405
0 < x | 0 0.127 0.567 0.694 0.876 1.000
M[X]=-0.405, M[Y]=2.736;
д) K[X,Y]=-0.098, R[X,Y]=-0.160;
е) X(i): -1 0
P{X=x(i)/Y= 5}: 0.576 0.424
M[X/Y= 5]=-0.576.
Вариант 13.
а) X: 1 2 3 | Y: -2 -1 0 1
P{X=Xi}: 0.210 0.546 0.244 |P{Y=Yi}:0.160 0.506 0.158 0.177
б) Зависимы.
в) P{X>Y}=0.933.
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 0.048 0.100 0.144 0.210
2<x<= 3| 0 0.093 0.540 0.642 0.756
3 < x | 0 0.160 0.665 0.823 1.000
M[X]=2.033, M[Y]=-0.648;
д) K[X,Y]=-0.027, R[X,Y]=-0.042;
е) X(i): 1 2 3
P{X=x(i)/Y= 2}: 0.104 0.780 0.116
M[X/Y= 2]=2.012.
Вариант 14.
а) X: 0 1 2 3 | Y: -2 -1 0 1
P{X=Xi}: 0.155 0.474 0.195 0.177 |P{Y=Yi}:0.171 0.486 0.185 0.158
б) Зависимы.
в) P{X>Y}=0.899.
г) \Y| y<=-2 |-2<y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y
_____ X_\|________|__________|__________|__________|__________
x<= 0 | 0 0 0 0 0
0<x<= 1| 0 0.034 0.087 0.122 0.155
1<x<= 2| 0 0.080 0.494 0.562 0.628
2<x<= 3| 0 0.123 0.574 0.701 0.823
3 < x | 0 0.171 0.657 0.842 1.000
M[X]=1.393, M[Y]=-0.670;
д) K[X,Y]=0.095, R[X,Y]=0.107;
е) X(i): 0 1 2 3
P{X=x(i)/Y= 2}: 0.186 0.180 0.317 0.317
M[X/Y= 2]=1.766.
Вариант 15.
а) X: 1 2 3 4 | Y: -1 0 1 2
3P{X=Xi}: 0.194 0.466 0.177 0.164 |P{Y=Yi}:0.152 0.404 0.135 0.169 0.141
б) Зависимы.
в) P{X>Y}=0.764.
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<= 2| 0 0.045 0.071 0.098 0.148 0.194
2<x<= 3| 0 0.084 0.411 0.482 0.579 0.659
3<x<= 4| 0 0.110 0.483 0.582 0.725 0.836
4 < x | 0 0.152 0.556 0.691 0.859 1.000
M[X]=2.311, M[Y]=0.742;
д) K[X,Y]=0.005, R[X,Y]=0.004;
е) X(i): 1 2 3 4
P{X=x(i)/Y= 1}: 0.201 0.323 0.212 0.265
M[X/Y= 1]=2.541.
Вариант 16.
а) X: 0 1 2 | Y: -2 -1 0 1
P{X=Xi}: 0.254 0.524 0.222 |P{Y=Yi}:0.182 0.464 0.192 0.161
б) Зависимы.
в) P{X>Y}=0.806.
г) \Y| y<=-2 |-2<y<=-1 |-1<y<= 0 |
0<y<= 1 | 1<y_____ X_\|________|__________|__________|__________|__________
x<= 0 | 0 0 0 0 0
0<x<= 1| 0 0.043 0.115 0.198 0.254
1<x<= 2| 0 0.127 0.525 0.667 0.778
2 < x | 0 0.182 0.647 0.839 1.000
M[X]=0.968, M[Y]=-0.668;
д) K[X,Y]=-0.046, R[X,Y]=-0.070;
е) X(i): 0 1 2
P{X=x(i)/Y= 1}: 0.345 0.345 0.310
M[X/Y= 1]=0.966.
Вариант
17.а) X: -1 0 | Y: -1 0 1
P{X=Xi}: 0.359 0.641 |P{Y=Yi}:0.182 0.509 0.310
б) Зависимы.
в) P{X>Y}=0.091.
г) \Y| y<=-1 |-1<y<= 0 | 0<y<= 1 | 1<y
_____ X_\|________|__________|__________|__________
x<=-1 | 0 0 0 0
-1<x<= 0| 0 0.091 0.216 0.359
0 < x | 0 0.182 0.690 1.000
M[X]=-0.359, M[Y]=0.128;
д) K[X,Y]=-0.006, R[X,Y]=-0.019;
е) X(i): -1 0
P{X=x(i)/Y= 3}: 0.500 0.500
M[X/Y= 3]=-0.500.
Вариант 18.
а) X: -1 0 | Y: 0 1
P{X=Xi}: 0.417 0.583 |P{Y=Yi}:0.333 0.667
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 0 | 0<y<= 1 | 1<y
_____ X_\|________|__________|__________
x<=-1 | 0 0 0
-1<x<= 0| 0 0.167 0.417
0 < x | 0 0.333 1.000
M[X]=-0.417, M[Y]=0.667;
д) K[X,Y]=0.028, R[X,Y]=0.120;
е) X(i): -1 0
P{X=x(i)/Y= 2}: 0.500 0.500
M[X/Y= 2]=-0.500.
Вариант 19.
а) X: -2 -1 | Y: 0 1 2 3 4
P{X=Xi}: 0.338 0.662 |P{Y=Yi}:0.156 0.479 0.122 0.124 0.119
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2<y<= 3 | 3<y<= 4 | 4<y
_____ X_\|________|__________|__________|__________|__________|__________
x<=-2 | 0 0 0 0 0 0
-2<x<=-1| 0 0.100 0.159 0.214 0.286 0.338
-1 < x | 0 0.156 0.634 0.757 0.881 1.000
M[X]=-1.338, M[Y]=1.573;
д) K[X,Y]=-0.062, R[X,Y]=-0.107;
е) X(i): -2 -1
P{X=x(i)/Y= 4}: 0.441 0.559
M[X/Y= 4]=-1.441.
Вариант 20.
а) X: -2 -1 0 1 | Y: 1 2
P{X=Xi}: 0.211 0.396 0.191 0.202 |P{Y=Yi}:0.373 0.627
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<= 1 | 1<y<= 2 | 2<y
_____ X_\|________|__________|__________
x<=-2 | 0 0 0
-2<x<=-1| 0 0.100 0.211
-1<x<= 0| 0 0.171 0.607
0<x<= 1| 0 0.262 0.798
1 < x | 0 0.373 1.000
M[X]=-0.616, M[Y]=1.627;
д) K[X,Y]=-0.070, R[X,Y]=-0.140;
е) X(i): -2 -1 0 1
P{X=x(i)/Y= 2}: 0.177 0.518 0.160 0.145
M[X/Y= 2]=-0.728.
Вариант 21.
а) X: -2 -1 | Y: -1 0 1
P{X=Xi}: 0.334 0.666 |P{Y=Yi}:0.286 0.457 0.258
б) Зависимы.
в) P{X>Y}=0.000.
г) \Y| y<=-1 |-1<y<= 0
| 0<y<= 1 | 1<y_____ X_\|________|__________|__________|__________
x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.143 0.243 0.334
-1 < x | 0 0.286 0.742 1.000
M[X]=-1.334, M[Y]=-0.028;
д) K[X,Y]=0.043, R[X,Y]=0.123;
е) X(i): -2 -1
P{X=x(i)/Y= 3}: 0.500 0.500
M[X/Y= 3]=-1.500.
Вариант 22.
а) X: -2 -1 0 | Y: -2 -1 0 1
P{X=Xi}: 0.226 0.515 0.259 |P{Y=Yi}:0.167 0.508 0.151 0.174
б) Зависимы.
в) P{X>Y}=0.170.
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 0.059 0.121 0.167 0.226
-1<x<= 0| 0 0.104 0.550 0.639 0.741
0 < x | 0 0.167 0.675 0.826 1.000
M[X]=-0.967, M[Y]=-0.668;
д) K[X,Y]=0.028, R[X,Y]=0.042;
е) X(i): -2
-1 0P{X=x(i)/Y= 1}: 0.339 0.250 0.411
M[X/Y= 1]=-0.927.
Вариант 23.
а) X: -1 0 1 | Y: -2 -1 0 1
P{X=Xi}: 0.245 0.478 0.277 |P{Y=Yi}:0.168 0.476 0.182 0.175
б) Зависимы.
в) P{X>Y}=0.660.
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<= 0| 0 0.056 0.111 0.174 0.245
0<x<= 1| 0 0.101 0.494 0.604 0.723
1 < x | 0 0.168 0.644 0.825 1.000
M[X]=0.032, M[Y]=-0.637;
д) K[X,Y]=-0.046, R[X,Y]=-0.066;
е) X(i): -1 0 1
P{X=x(i)/Y= 1}: 0.409 0.273 0.318
M[X/Y= 1]=-0.091.
Вариант 24.
а) X: -2 -1 0 1 2 | Y: 0 1 2
P{X=Xi}: 0.174 0.393 0.146 0.166 0.122 |P{Y=Yi}:0.227 0.520 0.253
б) Зависимы.
в) P{X>Y}=0.120.
г) \Y| y<= 0 | 0<y<= 1 | 1<y<= 2 | 2
<y_____ X_\|________|__________|__________|__________
x<=-2 | 0 0 0 0
-2<x<=-1| 0 0.056 0.118 0.174
-1<x<= 0| 0 0.103 0.471 0.566
0<x<= 1| 0 0.149 0.572 0.713
1<x<= 2| 0 0.192 0.671 0.878
2 < x | 0 0.227 0.747 1.000
M[X]=-0.331, M[Y]=1.027;
д) K[X,Y]=0.062, R[X,Y]=0.070;
е) X(i): -2 -1 0 1 2
P{X=x(i)/Y= 2}: 0.219 0.158 0.180 0.263 0.180
M[X/Y= 2]=0.026.
Вариант 25.
а) X: 1 2 3 4 5 | Y: 1 2
P{X=Xi}: 0.138 0.386 0.139 0.162 0.174 |P{Y=Yi}:0.366 0.634
б) Зависимы.
в) P{X>Y}=0.552.
г) \Y| y<= 1 | 1<y<= 2 | 2<y
_____ X_\|________|__________|__________
x<= 1 | 0 0 0
1<x<= 2| 0 0.071 0.138
2<x<= 3| 0 0.148 0.525
3<x<= 4| 0 0.204 0.663
4<x<= 5| 0 0.275 0.826
5 < x | 0 0.366 1.000
M[X]=2.848, M[Y]=1.634;
д) K[X,Y]=-0.089, R[X,Y]=-0.139;
е) X(i): 1 2 3 4 5
P{X=x(i)/Y= 1}: 0.195 0.210 0.152 0.195 0.248
M[X/Y= 1]=3.091.