Домашняя работа
по математической статистике
студента ФТФ – 33
Каменщикова Михаила
Вариант 1
Задание 1.1
Выборка А
0 |
4 |
2 |
0 |
5 |
1 |
1 |
3 |
0 |
2 |
2 |
5 |
2 |
4 |
2 |
5 |
3 |
1 |
5 |
2 |
0 |
2 |
2 |
3 |
2 |
3 |
2 |
2 |
1 |
3 |
0 |
|
5 |
5 |
3 |
2 |
2 |
0 |
2 |
1 |
1 |
2 |
4 |
3 |
2 |
5 |
3 |
|
2 |
3 |
4 |
3 |
2 |
3 |
2 |
4 |
2 |
2 |
6 |
3 |
3 |
3 |
5 |
|
хmin=0
xmax=6
R=6
N=61
xi |
mi |
ωi=mi/N |
Накопл. частости |
0 |
6 |
0,0984 |
0,098361 |
1 |
6 |
0,0984 |
0,196721 |
2 |
21 |
0,3443 |
0,540984 |
3 |
14 |
0,2295 |
0,770492 |
4 |
5 |
0,082 |
0,852459 |
5 |
8 |
0,1311 |
0,983607 |
6 |
1 |
0,0164 |
1 |
|
N=61 |
∑ = 1 |
|
|
0 |
x≤0 |
|
0,0984 |
0<x≤1 |
|
0,1967 |
1<x≤2 |
|
0,541 |
2<x≤3 |
F = |
0,7705 |
3<x≤4 |
|
0,8525 |
4<x≤5 |
|
0,9836 |
5<x≤6 |
|
1 |
x>6 |
Xср = 2.56
Sx2=2,1811
Sx=1,4769
M0=2
Mе=2
Выборка В
135 |
133 |
124 |
132 |
104 |
152 |
143 |
129 |
120 |
122 |
124 |
130 |
117 |
123 |
123 |
129 |
121 |
122 |
131 |
137 |
124 |
137 |
112 |
131 |
126 |
128 |
111 |
129 |
115 |
147 |
132 |
137 |
119 |
125 |
120 |
132 |
129 |
125 |
123 |
127 |
132 |
118 |
132 |
132 |
134 |
131 |
120 |
132 |
135 |
132 |
125 |
132 |
108 |
114 |
133 |
133 |
135 |
131 |
125 |
133 |
114 |
115 |
122 |
131 |
125 |
132 |
126 |
115 |
117 |
118 |
118 |
126 |
132 |
134 |
127 |
127 |
124 |
135 |
127 |
115 |
144 |
129 |
120 |
127 |
137 |
127 |
125 |
116 |
132 |
120 |
127 |
118 |
109 |
127 |
122 |
127 |
120 |
135 |
116 |
118 |
133 |
136 |
126 |
119 |
126 |
129 |
127 |
126 |
129 |
124 |
127 |
132 |
126 |
131 |
130 |
126 |
124 |
135 |
132 |
130 |
124 |
123 |
123 |
130 |
132 |
143 |
139 |
120 |
134 |
108 |
136 |
139 |
121 |
111 |
123 |
140 |
137 |
120 |
131 |
118 |
120 |
120 |
134 |
131 |
129 |
127 |
116 |
138 |
128 |
133 |
131 |
128 |
140 |
138 |
124 |
131 |
120 |
126 |
109 |
137 |
111 |
115 |
130 |
113 |
126 |
115 |
135 |
130 |
125 |
118 |
115 |
128 |
123 |
129 |
120 |
115 |
134 |
118 |
117 |
120 |
N=180
хmin=104
хmax=152
R=48
h=7
интервал |
mi |
ωi=mi/N |
Накопл. частости |
|
[a;b) |
|
|
|
|
100,5 |
107,5 |
1 |
0,005556 |
0,005556 |
107,5 |
114,5 |
11 |
0,061111 |
0,066667 |
114,5 |
121,5 |
39 |
0,216667 |
0,283333 |
121,5 |
128,5 |
52 |
0,288889 |
0,572222 |
128,5 |
135,5 |
58 |
0,322222 |
0,894444 |
135,5 |
142,5 |
14 |
0,077778 |
0,972222 |
142,5 |
149,5 |
4 |
0,022222 |
0,994444 |
149,5 |
156,5 |
1 |
0,005556 |
1 |
|
|
N = 180 |
∑ = 1 |
|
|
0,005556 |
100,5<x≤107,5 |
|
0,066667 |
107,5<x≤114,5 |
|
0,283333 |
114,5<x≤121,5 |
F(x) = |
0,572222 |
121,5<x≤128,5 |
|
0,894444 |
128,5<x≤135,5 |
|
0,972222 |
135,5<x≤142,5 |
|
0,994444 |
142,5<x≤149,5 |
|
1 |
149,5<x≤156,5 |
xср = 126,48
Sx2 = 68,05
Sx = 8,25
M0 = 129,34
ME = 126,75
Задание 1.2
F3 |
F4 |
43 |
52 |
51 |
42 |
44 |
40 |
47 |
38 |
34 |
37 |
F3 xi |
mi |
ωi |
|
F4 xi |
|
|
43 |
1 |
0,2 |
52 |
1 |
0,2 |
|
51 |
1 |
0,2 |
42 |
1 |
0,2 |
|
44 |
1 |
0,2 |
40 |
1 |
0,2 |
|
47 |
1 |
0,2 |
38 |
1 |
0,2 |
|
34 |
1 |
0,2 |
37 |
1 |
0,2 |
F3 |
F4 |
xcp = 43,8 |
xcp = 41,8 |
Sx2 = 31,76 |
Sx2 = 28,96 |
Sx = 5,64 |
Sx = 5,38 |
Задание 1.3
Выборка С
X |
Y |
Z |
X |
Y |
Z |
X |
Y |
Z |
X |
Y |
Z |
67 |
–201 |
582 |
82 |
–237 |
730 |
79 |
–226 |
697 |
90 |
–269 |
801 |
68 |
–199 |
602 |
70 |
–209 |
626 |
75 |
–218 |
672 |
95 |
–279 |
846 |
70 |
–206 |
645 |
83 |
–243 |
737 |
82 |
–245 |
729 |
88 |
–259 |
782 |
76 |
–221 |
674 |
80 |
–239 |
716 |
85 |
–247 |
763 |
86 |
–251 |
773 |
80 |
–238 |
718 |
76 |
–221 |
681 |
68 |
–201 |
608 |
71 |
–207 |
635 |
87 |
–256 |
811 |
81 |
–238 |
721 |
72 |
–215 |
643 |
77 |
–257 |
777 |
75 |
–222 |
668 |
76 |
–223 |
710 |
71 |
–209 |
637 |
73 |
–227 |
683 |
79 |
–230 |
702 |
81 |
–207 |
680 |
72 |
–212 |
638 |
82 |
–214 |
647 |
79 |
–234 |
701 |
80 |
–237 |
626 |
68 |
–203 |
611 |
74 |
–243 |
736 |
73 |
–217 |
648 |
76 |
–216 |
708 |
86 |
–252 |
773 |
67 |
–214 |
659 |
86 |
–253 |
773 |
70 |
–228 |
658 |
85 |
–251 |
764 |
82 |
–196 |
699 |
78 |
–228 |
682 |
79 |
–193 |
690 |
71 |
–206 |
632 |
72 |
–239 |
735 |
79 |
–230 |
708 |
74 |
–234 |
579 |
72 |
–214 |
641 |
74 |
–210 |
640 |
67 |
–201 |
596 |
77 |
–229 |
714 |
76 |
–227 |
675 |
77 |
–219 |
703 |
79 |
–237 |
702 |
65 |
–286 |
704 |
62 |
–286 |
587 |
79 |
–226 |
707 |
69 |
–211 |
609 |
84 |
–248 |
766 |
63 |
–186 |
588 |
|
|
|
Zmin = 579
Zmax = 846
N = 63
R = 267
h = 38
интервал |
mi |
ωi=mi/N |
Накопл. частости |
xi |
|
[a;b) |
|
|
|
|
|
560 |
598 |
5 |
0,079365 |
0,079365 |
579 |
598 |
636 |
8 |
0,126984 |
0,206349 |
617 |
636 |
674 |
12 |
0,190476 |
0,396825 |
655 |
674 |
712 |
18 |
0,285714 |
0,68254 |
693 |
712 |
750 |
9 |
0,142857 |
0,825397 |
731 |
750 |
788 |
8 |
0,126984 |
0,952381 |
769 |
788 |
826 |
2 |
0,031746 |
0,984127 |
807 |
826 |
864 |
1 |
0,015873 |
1 |
845 |
|
|
N = 63 |
∑ = 1 |
|
|
xcp = 688,17
Sx2 = 78450
Sx = 280
Задание 2.1
Выборка А |
Выборка В |
хср = 2,56 |
xср = 126,48 |
SH2 = 2,2175 |
SH2 =68,4302 |
SH = 1,4891 |
SH = 8,2723 |
Задание 2.2
F3 |
F4 |
xcp = 43,8 |
xcp = 41,8 |
SH2 = 39,7 |
SH2 = 36,2 |
SH = 6,3 |
SH = 6,02 |
Задание 2.3
xcp = 688,17
SH2 = 79715
SH = 282,3
Задание 2.4
1 – α = 0,95
F3 |
F4 |
xcp = 43,8 |
xcp = 41,8 |
SH = 6,3 |
SH = 6,02 |
N = 5 |
N = 5 |
→
= 1,96
Для F3
38,3<a<49,3
q(0.95; 4) = 1.34
0<σ<6.3(1+1.34)
0<σ<14.7
0≤ σ2 = D <216.1
Для F4
ε = 2,27
39,5<a<44.1
q(0.95; 4) = 1.34
0<σ<14.1
0≤ σ2 = D <198.8
Задание 2.5
1 – α = 0,99
ε = 0,1
t0,99; 4 =4,60
F3 |
F4 |
N = 84006 |
N = 76600 |
Задание 3.1
xi |
|
|
mi |
|
0 |
-2,56 |
-16,7772 |
6 |
-100,663296 |
1 |
-1,56 |
-3,79642 |
6 |
-22,778496 |
2 |
-0,56 |
-0,17562 |
21 |
-3,687936 |
3 |
0,44 |
0,085184 |
14 |
1,192576 |
4 |
1,44 |
2,985984 |
5 |
14,92992 |
5 |
2,44 |
14,52678 |
8 |
116,214272 |
6 |
3,44 |
40,70758 |
1 |
40,707584 |
|
|
|
|
∑ = 45,914624 |
M3 = 6,56
AS = 1,98