Ehtimolliklar nazariyasi va matematik statistika

Misol va masalalar
Quyidagi tanlanma uchun variatsion qator va statistik taqsi-motini yozing: 5, 7, 4, 3, 5, 10, 7, 4, 5, 7, 7, 9, 9, 10, 3, 5, 4, 7, 5, 10.
Javob: Variatsion qator:
3,3, 4, 4, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 10, 10, 10.

Statistik taqsimot:	x,:	3	4	5	7	9	10
		2	3	5	5	2	3

Yuqorida berilgan tanlanma uchun empirik taqsimot funk­ siyasini toping.
0, x < 3,
0,1, 3 < x < 4,
j 0,25, 4 < x < 5,

Javob: F2*0(x) = •{

0,5, 5 < x < 7,
0,75, 7 < x < 9,

_1, x > 9.
Quyidagi tanlanma uchun statistik taqsimotni yozing va chas­ totalar poligonini chizing: 1, 5, 4, 5, 4, 1, 3, 4, 7, 5, 4, 7, 3, 4, 5, 1, 1, 3, 7, 4, 5, 5, 4, 1, 3, 5, 4, 7, 5, 1, 4, 5, 3, 1, 4, 7, 1, 4, 3, 5, 1,4, 5, 5, 7, 3, 1,3, 4, 5.
5, 5, 4, 6, 5, 4, 6, 6, 9, 7, 10, 5, 6, 10, 7, 4, 4, 5, 4, 7, 5, 4,
6, 6, 5, 6, 10, 6, 5, 5 tanlanma berilgan boMsin. Tanlanmaning statistik taqsimoti, tanlanma o‘rta qiymati va tanlanma dispersiya­ sini toping.

Javob'.
Statistik taqsimot: x;. 4 5 6
n-. 6 9 8
= 5,9, DT = 0,29.
91 0

3 1 3

177

xx,x2 ,...,xn tanlanma berilgan bo'lsin. Tanlanma o‘rta qiyma-ti uchun quyidagi
2 > / - * ) = o

1=1

tenglik bajarilishini isbotlang.
Tanlanmaning statistik taqsimoti quyidagicha boMsin: Xf. x, x2 ... xk
nr «i «2 - nk
Tanlanma dispersiyasini hisoblash uchun quyidagi
DT = x-2' n<~ x 2
7=1

formula o‘rinli ekanligini ko‘rsating.
Berilgan tanlanma taqsimoti bo'yicha chastotalar gistogram­ masini tuzing.
Interval Interval
chastotalari
1-5 10
5-9 20
9-13 28
13-17 12
17-21 20
21-23 10
xux2,...,xn tanlanma berilgan. Bosh to'plamning matematik kutilmasi m ning bahosi sifatida w, = x, statistik baho taklif qilin­ gan. Bu bahoning siljimaganligi va asosliligini tekshiring.
Bosh to'plam X parametrli Puasson qonuni bo'yicha taqsimlangan bo'lib, bu to'plam bo'yicha tanlanma tuzilgan bo'lsin. X parametr uchun tanlanma o'rta qiymati siljimagan va asosli baho bo'lishini ko'rsating.

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