§. Mustaqil yechish uchun misol va masalalar
variant 1.Tanlanma taqsimot berilgan:
xi 3 5 6 8
ni 9 15 16 10
Nisbiy chastotali taqsimoti yozilsin
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 4 6 9
ni 12 18 24
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 1,2
wi 0 ,2
2,6
0 ,3
3,4
0 ,4
5
0 ,1
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi va- riantalar chastota- lari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
2-4
4-6
6-8
8-10
10-12
12-14
14-16
|
8
12
18
22
20
12
8
|
4
6
9
11
10
6
4
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
1 5
12 8
7 10
17 13
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring.
Еmpirik chastotalar:
ni : 7 ,
39,
76 ,
104,
81,
32,
30, 13
Nazariy chastotalar:
ni :
6 , 13,
43,
75,
98,
79,
52, 12
H 0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligi va ularga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha na- zariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi 1
|
hi
|
1
2
|
1
4
|
4
7
|
14
22
|
3
4
5
6
7
8
9
|
7
10
13
16
19
22
25
|
10
13
16
19
22
25
28
|
26
32
36
26
18
16
10
|
variant 1.Tanlanma taqsimot berilgan:
xi 6
ni 14
8 9 12
10 10 16
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 3
ni 16
8 14
32 22
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2
wi 0 ,23
3,5
0 ,2
5
0 ,36
6 ,5
0 ,21
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi variantalar
chastotalari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
|
3-6
|
6
|
2
|
2
|
6-9
|
12
|
4
|
3
|
9-12
|
18
|
6
|
4
|
12-15
|
21
|
7
|
5
|
15-18
|
15
|
5
|
6
|
18-21
|
12
|
4
|
7
|
21-24
|
6
|
2
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖: chastota 𝑛 𝑖:
2 4 7 12
18 10 11 11
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
5, 13,
36 ,
72,
102,
84,
31, 12
Nazariy chastotalar:
ni :
6 , 14,
40,
86 ,
90,
52,
16 , 9
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligi va ularga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha na- zariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi 1
|
hi
|
1
|
4
|
8
|
16
|
2
|
8
|
12
|
24
|
3
|
12
|
16
|
22
|
4
|
16
|
20
|
30
|
5
|
20
|
24
|
26
|
6
|
24
|
28
|
24
|
7
|
28
|
32
|
22
|
8
|
32
|
36
|
20
|
9
|
36
|
40
|
16
|
variant 1.Tanlanma taqsimot berilgan:
xi 1
ni 12
3 6 8
11 14 13
Nisbiy chastotali taqsimoti yozilsin.
Berilgan tanlanma taqsimotga ko‗ra еmpirik funksiya tuzing:
xi 4 0 6
ni 15 20 25
Tanlanmaning quyida berilgan taqsimoti bo‗yicha nisbiy chasto- talar poligonini yasang:
xi 2
wi 0 ,22
4
0 ,33
7
0 ,26
9
0 ,19
Tanlanmaning quyida berilgan taqsimoti bo‗yicha chastotalar gistogrammasini yasang:
Interval nomeri
|
Qismiy interval
|
Intervaldagi variantalar chastotalari yig‗indisi
|
Chastota zichligi
|
i
|
xi 1 xi
|
ni
|
ni h
|
1
2
3
4
5
6
7
|
4-8
8-12
12-16
16-20
20-24
24-28
28-32
|
8
16
28
36
26
16
10
|
2
4
7
9
6,5
4
2,5
|
Bosh to‗plamdan hajmi n=100 ga teng tanlanma olingan va taq- simoti yozilgan:
varianta 𝑥 𝑖:
chastota 𝑛𝑖:
6 9 12 14
10 14 12 14
Bosh to‗plamning o‗rta qiymati uchun siljimagan baho topilsin.
0,05 . H0 gipotezani tekshiring. Еmpirik chastotalar:
ni :
8, 15,
39,
72,
106 ,
84,
35, 12
Nazariy chastotalar:
ni :
6 , 14,
42,
91,
89,
46 ,
18, 10
H0 : bosh to‗plam normal taqsimlangan.
Bosh to‗plam normal taqsimlangan deb faraz qilib, n=200 hajmli tanlanmaning, bir xil uzunlikdagi intervallar ketma-ketligiva ularga mos chastotalar ko‗rinishida berilgan еmpirik taqsimoti bo‗yicha na- zariy chastotalarini toping.
Interval nomeri
|
Interval uchlari
|
Chastotalar
|
i
|
xi
|
xi 1
|
hi
|
1
|
4
|
6
|
13
|
2
|
6
|
8
|
26
|
3
|
8
|
10
|
24
|
4
|
10
|
12
|
32
|
5
|
12
|
14
|
28
|
6
|
14
|
16
|
22
|
7
|
16
|
18
|
18
|
8
|
18
|
20
|
20
|
9
|
20
|
22
|
17
|
variant 1.Tanlanma taqsimot berilgan:
xi 5
Do'stlaringiz bilan baham: |