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The pair has the joint distribution (in m-file npr08_07.m ):
t = | -3.1 | -0.5 | 1.2 | 2.4 | 3.7 | 4.9 |
u = 7.5 | 0.0090 | 0.0396 | 0.0594 | 0.0216 | 0.0440 | 0.0203 |
4.1 | 0.0495 | 0 | 0.1089 | 0.0528 | 0.0363 | 0.0231 |
-2.0 | 0.0405 | 0.1320 | 0.0891 | 0.0324 | 0.0297 | 0.0189 |
-3.8 | 0.0510 | 0.0484 | 0.0726 | 0.0132 | 0 | 0.0077 |
Determine the marginal distributions and the corner values for . Determine and .
npr08_07 Data are in X, Y, P
jcalcEnter JOINT PROBABILITIES (as on the plane) P
Enter row matrix of VALUES of X XEnter row matrix of VALUES of Y YUse array operations on matrices X, Y, PX, PY, t, u, and P
disp([X;PX]')
-3.1000 0.1500-0.5000 0.2200
1.2000 0.33002.4000 0.1200
3.7000 0.11004.9000 0.0700
disp([Y;PY]')
-3.8000 0.1929-2.0000 0.3426
4.1000 0.27067.5000 0.1939
jddbnEnter joint probability matrix (as on the plane) P
To view joint distribution function, call for FXYdisp(FXY)
0.1500 0.3700 0.7000 0.8200 0.9300 1.00000.1410 0.3214 0.5920 0.6904 0.7564 0.8061
0.0915 0.2719 0.4336 0.4792 0.5089 0.53550.0510 0.0994 0.1720 0.1852 0.1852 0.1929
M = (1<=t)&(t<=4)&(u>4);
P1 = total(M.*P)P1 = 0.3230
P2 = total((abs(t-u)<=2).*P)
P2 = 0.3357
The pair has the joint distribution (in m-file npr08_08.m ):
t = | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 |
u = 12 | 0.0156 | 0.0191 | 0.0081 | 0.0035 | 0.0091 | 0.0070 | 0.0098 | 0.0056 | 0.0091 | 0.0049 |
10 | 0.0064 | 0.0204 | 0.0108 | 0.0040 | 0.0054 | 0.0080 | 0.0112 | 0.0064 | 0.0104 | 0.0056 |
9 | 0.0196 | 0.0256 | 0.0126 | 0.0060 | 0.0156 | 0.0120 | 0.0168 | 0.0096 | 0.0056 | 0.0084 |
5 | 0.0112 | 0.0182 | 0.0108 | 0.0070 | 0.0182 | 0.0140 | 0.0196 | 0.0012 | 0.0182 | 0.0038 |
3 | 0.0060 | 0.0260 | 0.0162 | 0.0050 | 0.0160 | 0.0200 | 0.0280 | 0.0060 | 0.0160 | 0.0040 |
-1 | 0.0096 | 0.0056 | 0.0072 | 0.0060 | 0.0256 | 0.0120 | 0.0268 | 0.0096 | 0.0256 | 0.0084 |
-3 | 0.0044 | 0.0134 | 0.0180 | 0.0140 | 0.0234 | 0.0180 | 0.0252 | 0.0244 | 0.0234 | 0.0126 |
-5 | 0.0072 | 0.0017 | 0.0063 | 0.0045 | 0.0167 | 0.0090 | 0.0026 | 0.0172 | 0.0217 | 0.0223 |
Determine the marginal distributions. Determine and .
npr08_08 Data are in X, Y, P
jcalc- - - - - - - - -
Use array operations on matrices X, Y, PX, PY, t, u, and Pdisp([X;PX]')1.0000 0.0800
3.0000 0.13005.0000 0.0900
7.0000 0.05009.0000 0.1300
11.0000 0.100013.0000 0.1400
15.0000 0.080017.0000 0.1300
19.0000 0.0700disp([Y;PY]')-5.0000 0.1092
-3.0000 0.1768-1.0000 0.1364
3.0000 0.14325.0000 0.1222
9.0000 0.131810.0000 0.0886
12.0000 0.0918F = total(((t<=10)&(u<=6)).*P)
F = 0.2982P = total((t>u).*P)
P = 0.7390
Data were kept on the effect of training time on the time to perform a job on a production line. X is the amount of training, in hours, and Y is the time to perform the task, in minutes. The data are as follows (in m-file npr08_09.m ):
t = | 1 | 1.5 | 2 | 2.5 | 3 |
u = 5 | 0.039 | 0.011 | 0.005 | 0.001 | 0.001 |
4 | 0.065 | 0.070 | 0.050 | 0.015 | 0.010 |
3 | 0.031 | 0.061 | 0.137 | 0.051 | 0.033 |
2 | 0.012 | 0.049 | 0.163 | 0.058 | 0.039 |
1 | 0.003 | 0.009 | 0.045 | 0.025 | 0.017 |
Determine the marginal distributions. Determine and .
npr08_09 Data are in X, Y, P
jcalc- - - - - - - - - - - -
Use array operations on matrices X, Y, PX, PY, t, u, and Pdisp([X;PX]')1.0000 0.1500
1.5000 0.20002.0000 0.4000
2.5000 0.15003.0000 0.1000
disp([Y;PY]')
1.0000 0.09902.0000 0.3210
3.0000 0.31304.0000 0.2100
5.0000 0.0570F = total(((t<=2)&(u<=3)).*P)
F = 0.5100P = total((u./t>=1.25).*P)
P = 0.5570
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