Чепуренко В.А. Учебное пособие по курсу Теория вероятности

n = 180

A = {

}

}

B = {

p =

1

36

P

5

P

5

m

1

m

35

180−m

4

1

4

35

176

= 0.17694

P (A) = P180 (4) = C180

36

36

(B) =

P

180 (m) =

P

C180

36

= 0.61597

36

m=0

m=0

λ = np = 5

P (A) ≈

54

e−5 = 0.17547 P (B) ≈

4!

5

Δ(A) ≈ 54!4 e−5·

≈

P

5m

e−5 = 0.61596

m!

m=0

·

− 360

= 0.00146 Δ(B) ≈ m=0

m! e−

·

360

= 0.00780

4 (5−4)2

5

5m

5

m−(5−m)2

Δ(B)P

√

x =

4−5

= 0.45356qP(A)

·0.163

0−0.5−5

=

2.49457

a =

σ =

180

·

1

3635

=

5

7

= 2.20479

36

6

≈

2.20479

−

2.20479

b

=

5+0.5−5

= 0.22678

P(B)

≈

Φ(0.22678)

−

Φ(

−

2.49457) =

2.20479

Pn(m)

0.15

0.10

B(n, p)

0.05

P (λ)

N

λ, σ2

0.00

m

0

2

4

6

8

10

B(n, p)

P (λ)

N λ, σ2

n = 180

p = 361

λ = np

σ2 = npq

p

A B

kA =

p

1−p

kB

p = 1

p = 1

2

5

n

p1, p2, ..., ps

(s > 2)

s

A1, A2, ..., As

s = 2

n

A1, A2, ..., As

m1, m2, ..., ms (m1 + m2 + ... + ms = n)

Pn (m1, m2, ..., ms) =

n!

× p1m1

× p2m2

× ... × psms ,

m1!m2!...ms!

s

s

P

P

mi = n

pi = 1

i=1

i=1

A = {

} B = {

A = {

}

B = {

}

C = {

}

n =

p1

p2

p3

[0; 10]

Ci,j,k,l = {

[0; 1]

i

[1; 3]

j

}

[3; 7]

k

[7; 10]

l

C1,2,3,4 = {

} {

}

C2,2,3,3

{

}

{

}

N

n

P (µ0 (n, N) = k)

µ0 (n, N)

k kJ J kL L

kN

N

n

A

K K K K N

A

(m1; m1 + m2; n1; n1 + n2) =

Cnm1 Cnm2

Cm1

+m2

1

2

(m; n; p; δ) =

m Ci piqn−i,

n1+n2

δ = 1

Cnmpmqn−m,

δ = 0

i=0

n

q = 1

−

p

P

(n; p; α) = z

z

z

(p; m; σ) = z

z

P

Cmpmqn−m

> α

q = 1

−

p

m=0

n

z−m

Φ

z−m

=

1

σ

e−

x2

dx = p

R

2

(p; 0; 1) = z

z

σ

(p) =

√2π −∞

Φ (z) =

1

z e−

x2

dx = p

2

R

(x−m)2

√2π −∞

δ = 1

(x; m; σ; δ) = ( Φ2πx−m ,

√1

e−

2σ2

,

δ

= 0

(x;

) =

σ

δ

(x; 0; 1; δ) =