Чепуренко В.А. Учебное пособие по курсу Теория вероятности

= p(1 − p)(3 −3!2p)

PH2 (A) =

1 − (1 − p)2

(1−p)+(1 − p)2 p =

2

H3

P (H3) = 33 =

9

1

2

3

PH3 (A) = C31p1(1 − p)2 = 3p(1 − p)2

p

= 9 27 45p + 19p2

A

6p

6p

p

(A) =

p

3 − 3p + p

2

+

3 − 5p + 2p

2

+

1

− 2p + p

2

=

9

9

9

P

−

3 3p+p2

6(3−5p+2p2)

PA (H1) =

−

2

PA (H2) =

27−45p+19p

2

227−45p+19p

PA (H3) =

6(1−2p+p

)

27−45p+19p2

6(2−p)(1−p)

P

(H2)

−

P

(H3) =

> 0

0

6

p < 1

A

A

27 45p+19p2

−

0 6 p < 27−√

P

A

(H

)

−

P

(H

) =

11p2−27p+15

> 0

69

2

A

1

27 45p+19p2

22

−

√

P

A

(H

) =

P

A

(H

)

p =

27− 69

≈

0.78

P

(H

) < P

A

(H

)

2

√

1

22

A

2

1

27− 69 < p 6 1

22

5p2−9p+3

9−√

P

A

(H

)

−

P

A

(H

) =

> 0

0 6 p <

21

3

1

27 45p+19p2

10

−

√

P

A

(H ) =

P

A

(H

)

p =

9− 21

≈

0.44

P

(H

) < P

(H

1

)

3

√

1

10

A

3

A

9− 21

< p 6 1

10

√

0 6 p <

9− 21

PA (H2) > P√A (H3) > PA (H1)

10

p =

9− 21

PA (H2) > PA (H3) = PA (H1)

√

34

√

9− 21

< p <

27− 69

PA (H2) > PA (H1) > PA (H3)

10

22

√

p =

27− 69

PA (H1) =

PA (H2) > PA (H3)

√

22

27− 69 < p < 1

PA (H1) > PA (H2) > PA (H3)

22

√

p < 27−

69

≈

0.78

√

22

H2

p >

27− 69

H1

p→0

22

<

p→0

A (H3) =

9

=

A (H1) = 9

lim

P

1

lim

P

2

= p→0

A (H2) = 3

lim

P

2

Ai = {i

}

PA1 (A2) PA1 (A3)

PA1A2 (A3) PA1

(A3)

A2

PA2 (A1) P

(A1)

A2

P

(A1) PA2A3 (A1)

A1+A3

N

N

N

Pk (t)

lim

Pk (t) = πk k = 0, 1, 2

t→∞

N

M3

− N

−

− N

N1 −

−

M1

−

N2

M2

N3

N

N

n

N − M −

A

M −

N − M − N

A = {

}

}

A = {

A = {

k

}

A = {

k

}

Pk (t)

t

Pk (t) = πk

θ =

α

k −1

lim

β

< 1

t→∞

2

1

3

3

A

B

B

A

z (N − z)

A

A

B

1 6 z 6 N − 1

p = P (

)

A

A

;

;

;

;

;

;

;

;

;

;

;

;

X

Y

X

Y

p1

p2

(p2 < p1)

p1 + p2 6= 1

α = p1/p2

Hl = {

}

¯

}

Hr = Hl = {

P (H A) =

p1 · 0.5

=

α

> 0.5.

p1 · 0.5 + p2 · 0.5

α + 1

l|

k2

− n2

−

N

k1

−

n1 −

N

m

A

B

C