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Обнинский институт атомной энергетики НИЯУ МИФИ

Предмет:

Теория вероятностей и математическая статистика

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Чепуренко В.А. Учебное пособие по курсу Теория вероятности

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20.01.2021

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<<< < Предыдущая 1 2 3 4 5 6 7 8 9 1011 / 1311 12 13 > Следующая >>>


k1	n1	k2	n2	m	A	B	C


					N
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						N	N N

						N	N
					N
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					N
					N
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					N
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					N	N	N N
						N	N

					N	N	N

							N N
							N

							N N

					N
							N

							N N




N

		N

			N
		N N
N		N N
N	N	N
	N
		N N

		N

N		N N
	N		N


	N		N

	N	N N

	n
		p
	A
	n	A
m	µn	m

Pn (m) = P (µn = m) = Cnmpmqn−m,

p = P (A) q = 1 − p

		p (n + 1)						p (n + 1) − 1,							p (n + 1) Z.
k0 =						[p (n + 1)] ,									p (n + 1)		/	Z
Pn(m)								Pn(m)							Pn(m)
0.15								0.15							0.15
								0.10
								0.10
0.10								0.05							0.10
0.05															0.05
0.05															0.05
0.00							m	0.00							m 0.00							m
0.00							m	0.00							m 0.00							m
0	5	10	15	20	25	30		0	5	10	15	20	25	30	0	5	10	15	20	25	30

n = 30

p = 0.2 p = 0.5 p = 0.8

A = {						n = 5							}		B = {
A = {		{										9	}		B = {
P (B) = C5			9		9			+ C5				9			9			+ C5		9		9		=	59049	=
} C =			P (A) = C							1	4		1	32			}4		= 5·854	=		20480		= 0.34683
			P (A) = C							1	36			32					= 5·854	=		20480		= 0.34683
= 0.35769									5		36			36					9			59049
= 0.35769										5	9			9					59049	= 0.
	1		1	1	8		4			3		1	3		8		2		5	1	5	8	0		21121
							−
	P (C) = 1								C	0	1	0		8		5	=		26281			44507
	P (C) = 1								C								=					44507

									A	B
n = 5
P (A) = 0.8 P (B) = 0.9
C = {A				B						B}	} D =
= {					A					B}	Ak = {A
			}	Bk = {B							Ak = {A
	k	5	}	Bk = {B		5	i−1			k	}; k = 0, 1, ..., 5
	5	P			5	P P				5	(19)
C =			AkBk D =					BiAj			P (C) =
		k=0				i=1 j=0
= P k=0 AkBk				=	k=0 P (AkBk) =					k=0 P (Ak) P (Bk) =
(19) 5	P	2	1		P		5	i 1		P
P	5	i	1				5	i 1	= 0.34321
=	C5k		(0.8 · 0.9)k (0.2 ·				0.1)5−k		= 0.34321
k=0		−		(Bi) P (Aj ) =				−	Ci Cj0.9i0.8j 0.15−i0.25−i =
P (D) =		−	P	(Bi) P (Aj ) =				−	Ci Cj0.9i0.8j 0.15−i0.25−i =
	P P						P P		5	5
	i=1 j=0						i=1 j=0

5i−1

=0.025 P P C5i C5j9i4j = 0.48746

i=1 j=0

A = {	B = {	n	}
	B = {	n
}	P (B) = C1p1qn−1		= npqn−1
}	1	n
P (AB) = qpqn−2 = pqn−1	PB (A) = n		{
	}		{
	}
ξi	i
A	P (A) = P00\|111

p0 = P{ξ1=0} (A) p1 = P{ξ1=1} (A)

P (A) = qp0 + pp1.

p1				P{i;j} (A) = P{ξ1=i;ξ2=j} (A)
p1	=	P{1;0} (A) ·					P (ξ2	= 0) + P{1;1} (A) · P	(ξ2	= 1)
p0	=	P{0;0} (A) ·					P (ξ2	= 0) + P{0;1} (A) · P	(ξ2	= 1)
P{ξ1=0;ξ2=0} (A) = 1
P{ξ1=0;ξ2			=1} (A) = P{ξ1=1} (A) = p1
P{ξ1=1;ξ2			=0} (A) = P{ξ1=0} (A) = p0
ξ2							ξ1
P{ξ1=1;ξ2			=1} (A) = P{ξ1=1;ξ2=1;ξ3=0} (A) · P (ξ3 = 0) +
+0 · P (ξ3 = 0) = P{ξ1=0} (A) · p = p0q
							q
−q(1 + p)p0 + p21 = 0								p0, p1
	p0	− pp1				= q
	q(1	p )
				q		q (1+p)
(p0; p1) =				q+p3	;	q+p3
		3
P (A) =	− 3
	q+p

		n
	Q(n)
Q(n)
5M	M
Q(n)	n
	Q(n)	M = 3 M = 10 n
		Q(n)
	n

			n
		p
m + l		l		l
	m + l		m
k	l

	n	Ak = {		k
	}	Bm	m {	m
			=	m
}		PBm (Ak) =	n

n = 7 n = 8

				2n
				p
	m + n
				m + n
k		λk	e−λ	λ > 0
k			e−λ	λ > 0
		k!		p
				p
				s

mn − m

n = 4, m = 1 n = 5, m = 1 n = 7, m = 2 n = 2m

A	A
	A
	A

A = {	} A =
= {	} A = {
	}
	{

}{

}

(r = 0, 1, 2, ..., n)

µn	n
	p 0; 1


K	N	A

x > 0

− p

= 1.

n→∞

lim

µn

n → ∞ p → 0

np → λ

m = 0, 1, ...

λm

P (µn = m) →

e−λ.

+ O n2

(µn = m) = m! e−

· 1 +

−

λm

(λ−m)2

= P (µn = m)

λm

e−λ

λm

e−λ

m − (λ − m)2

− m!

≈ m!

<<< < Предыдущая 1 2 3 4 5 6 7 8 9 1011 / 1311 12 13 > Следующая >>>


k1	n1	k2	n2	m	A	B	C


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k1	n1	k2	n2	m	A	B	C


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k1	n1	k2	n2	m	A	B	C


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							N N
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					N
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							N N