Bài giảng Xác suất Thống kê và ứng dụng Tác giả: Phan Thanh Hồng, Trường Đại học Thăng Long, 2009

8/21/2019 Bi ging Xc sut Thng k v ng dng Tc gi: Phan Thanh Hng, Trng i hc Thng Long, 2009

1/824
http://find/


2/824
http://find/


3/824
http://find/


4/824
http://find/


5/824
http://find/


6/824
http://find/


7/824
http://find/


8/824
http://find/


9/824
http://find/


10/824
http://find/


11/824
http://find/


12/824
http://find/


13/824
http://find/


14/824
http://find/


15/824
http://find/


16/824
http://find/


17/824
http://find/


18/824
http://find/


19/824
http://find/http://goback/


20/824
http://find/


21/824
http://find/


22/824
http://find/


23/824
http://find/


24/824
http://find/


25/824
http://find/


26/824
http://find/


27/824
http://find/


28/824
http://find/


29/824
http://find/


30/824
http://find/


31/824
http://find/


32/824
http://find/


33/824


34/824
http://find/


35/824
http://find/


36/824
http://find/


37/824
http://find/


38/824
http://find/


39/824
http://find/


40/824
http://find/


41/824
http://find/


42/824
http://find/


43/824
http://find/


44/824
http://find/


45/824
http://find/


46/824
http://find/


47/824
http://find/


48/824
http://find/


49/824
http://find/


50/824
http://find/


51/824
http://find/


52/824
http://find/


53/824
http://find/


54/824
http://find/


55/824
http://find/


56/824
http://find/


57/824
http://find/


58/824
http://find/


59/824
http://find/


60/824
http://find/


61/824
http://find/


62/824
http://find/


63/824
http://find/


64/824
http://find/


65/824
http://find/


66/824
http://find/


67/824
http://find/


68/824
http://find/


69/824
http://find/


70/824
http://find/


71/824
http://find/


72/824
http://find/


73/824
http://find/


74/824
http://find/


75/824
http://find/


76/824
http://find/


77/824
http://find/


78/824

100%
http://find/


79/824
http://find/


80/824
http://find/


81/824
http://goforward/http://find/http://goback/


82/824


83/824


84/824


85/824


86/824

k

k

k

2n

1 3

k

2k n n

h

h

Xmax Xmin

k

Xmin Xmax

h

Xmin

Xmax


87/824

k

k

k

2n

1 3

k

2k n n

h

h

Xmax Xmin

k

Xmin Xmax

h

Xmin

Xmax
http://find/


88/824

k

k

k

2n

1 3

k

2k n n

h

h

Xmax Xmin

k

Xmin Xmax

h

Xmin

Xmax
http://find/


89/824

Xmin Xmin h

Xmin h Xmin 2h

Xmin 2h Xmin 3h

xi

xi
http://find/


90/824

Xmin Xmin h

Xmin h Xmin 2h

Xmin 2h Xmin 3h

xi

xi
http://find/


91/824

K

7 27 65

Xmin 10 Xmax 29 h 29

10

7
http://find/


92/824


93/824


94/824


95/824


96/824
http://find/


97/824
http://find/


98/824
http://find/


99/824
http://find/


100/824


101/824


102/824


103/824


104/824
http://find/


105/824


106/824
http://find/


107/824


108/824
http://find/


109/824

#

#

#
http://find/


110/824

#

#
http://find/


111/824

a, b

a, b
http://find/


112/824
http://find/


113/824

#

#

#

49

500
http://find/


114/824

49
http://find/


115/824

29.8 33.3

29, 30, 31, 32, 33
http://find/


116/824

49


117/824


118/824

5 20
http://find/


119/824
http://find/


120/824
http://find/


121/824


122/824

Bieu do tan so

Thoi gian

Tan

so

10 15 20 25 30 35

0

5

10

15

20

25

Bieu do tan suat

Thoi gian

Tan

suat

10 15 20 25 30 35

0.0

0

0.0

5

0.

10

0.1

5


123/824
http://find/


124/824
http://find/


125/824


126/824

Bieu do tan so v da giac tan so Da giac tan so


127/824

Thoi gian

Tan

so

10 15 20 25 30 35

0

5

10

15

20

25

10 15 20 25 30

0

5

10

15

20

Thoi gian

Tan

so


128/824
http://find/


129/824
http://find/


130/824
http://find/


131/824

55%

22%

11%

10%

2%


132/824

55%

22%

11%

10%

2%

than da

55%


133/824

55%

22%

11% 10%

2%

55%

nang luong hat nhan

22%khi ga tu nhien

11%

thuy dien

10%

dau hoa

2%


134/824

100
http://find/


135/824

do thi thanh

2

5

energy


136/824

1 2 3 4 5 6 7

0

5

10

15

20

gyindustrialretailhealth carefinancialtechnologyother


137/824

1

2

3

4

5

6

7

0 5 10 15 20 25

energyindustrialretailhealth care

financialtechnologyother
http://find/


138/824
http://find/


139/824
http://find/


140/824
http://find/


141/824


142/824


143/824


144/824
http://find/


145/824

200

1.0
http://find/


146/824

value

0

50

100

150

0.5

0.6

0.7

0.8

0.9

T

an

suattich

luy

nhua do day vo quai nhan bac mau khac
http://find/


147/824

y

y

y
http://find/


148/824


149/824

33.5


150/824

10.0 10.5 11.0 11.5 12.0

32.0

32.5

33.0

3

LuongXB135

Donhot
http://find/


151/824

y

x
http://find/


152/824
http://find/


153/824


154/824
http://find/


155/824
http://find/


156/824
http://find/


157/824
http://find/


158/824


159/824


160/824


161/824


162/824
http://find/


163/824

.

.

.

.

.

.
http://find/


164/824
http://find/


165/824

, , . . . ,


166/824

. . . . .

.


167/824

,

, . . . ,

,

, . . . ,


168/824

.

.

.

.

.

.

.

.
http://find/


169/824

.

.

.

.

.

.

.

.
http://find/


170/824
http://find/


171/824
http://find/


172/824
http://find/


173/824
http://find/


174/824
http://find/


175/824

Hinh a Hinh b Hinh c
http://find/


176/824

Mo=Md=TB Mo


177/824

Mo=Md=TB Mo


178/824

Trung tam A

Thoi gian sua (ngay)

tan

so

0 2 4 6 8

0

2

4

6

8

Trung tam B

Thoi gian sua (ngay)

tan

so

0 2 4 6 8

0

2

4

6

8
http://find/


179/824
http://find/


180/824


181/824


182/824
http://find/


183/824

.
http://find/


184/824

. .

. .

. .

.

.

.

.

.

.

.
http://find/


185/824
http://find/


186/824
http://find/


187/824
http://find/


188/824

.

.

.
http://find/


189/824

.

.

.
http://find/


190/824
http://find/


191/824

%

%
http://find/


192/824
http://find/


193/824

.
http://find/


194/824

%
http://find/


195/824

.

.
http://find/


196/824

.

.
http://find/


197/824

%

Bieu do hop va rau cua mau 65 tgtt


198/824

10 15 20 25 30

%
http://find/


199/824

%

%
http://find/


200/824

%


201/824

%

%

,


202/824

%

,

.

%

,


203/824

68%

++

95%

2 ++ 2

99.7%

3 ++ 3


204/824

. .

,

. ,

.

%
http://find/


205/824

,

. ,

.

%

,

. ,

.

.

%
http://find/


206/824

%

,
http://find/


207/824
http://find/


208/824
http://find/


209/824


210/824


211/824


212/824
http://find/


213/824


214/824
http://find/


215/824
http://find/


216/824
http://find/


217/824
http://find/


218/824
http://find/


219/824


220/824
http://find/


221/824
http://find/


222/824
http://find/


223/824
http://find/


224/824
http://find/


225/824

0, 1 1

0

0

1
http://find/


226/824

1

A P A
http://find/


227/824
http://find/


228/824
http://find/


229/824
http://find/


230/824
http://find/


231/824
http://find/


232/824
http://find/


233/824

S, N

1, 2, 3, 4, 5, 6

0, 1, 2, . . . , 100

0, 1, 2 . . .
http://find/


234/824

S, N

1, 2, 3, 4, 5, 6

0, 1, 2, . . . , 100

0, 1, 2 . . .

A 2, 4, 6

T

G
http://find/


235/824

G

TT,TG,GT,GG

B

B GT,TG,GG

A 2, 4, 6

T

G
http://find/


236/824

G

TT,TG,GT,GG

B

B GT,TG,GG

A 2, 4, 6

T

G
http://find/


237/824

TT,TG,GT,GG

B

B GT,TG,GG
http://find/


238/824

A A

A
http://find/


239/824

A A

A
http://find/


240/824

n

A

A A
http://find/


241/824

P

A

P S P N 1

2 0.5
http://find/


242/824

52 A

A

P A 4

52

P S P N 1

2 0.5
http://find/


243/824

52 A

A

P A 4

52

A

A

0

1

52

A 2
http://find/


244/824

C252

A C24

P A C2

4

C252

0.0045

A

A

0

1

52

A

C2
http://find/


245/824

C252

A C24

P A C2

4

C252

0.0045

A

A

0

1

52

A

C2
http://find/


246/824

C252

A C24

P A C2

4

C252

0.0045

A m

n

n

m A

A


247/824

A n

m

n

A

10 100 10000 6 47

5067

S

6 10 0.6 47 100 0.47 5067 10000 0.5067

S

0.5 P S 0.5


248/824

10 100 10000 6 47

5067

S

6 10 0.6 47 100 0.47 5067 10000 0.5067

S

0.5 P S 0.5
http://find/


249/824


250/824


251/824

A A

A A A

P A A


252/824

A A

P A 1 P A

A

A
http://find/


253/824

A A

P A C2

3

C27

0.143

P A 1 P A 0 857
http://find/


254/824

P A 1 P A 0.857

A B

A B A

B A B A B P A B

A B

A

B

A

B A B A B P A B A
http://find/


255/824

A B AB A B A B P A B A

B

A

B
http://find/


256/824

A B A

B

P A B P A P B P A B A

B
http://find/


257/824

A

B

P A B

P A 4

52 P B

26

52 P A B

2

52
http://find/


258/824

P A B P A P B P A B 4

52

26

53

2

52

28

52 0.538

A

B

P A B

P A 4

52 P B

26

52 P A B

2

52
http://find/


259/824

P A B P A P B P A B 4

52

26

53

2

52

28

52 0.538

A B

A B
http://find/


260/824

A B

A B

P A B P A P B

A B
http://find/


261/824

A1, A2, . . . , An

A1, A2, . . . , An A1 A2 An

A1 A2 An

Ai i 1, n

A1, A2, . . . , An A1 A2 An

A1A2 . . . An Ai i 1, n

A A A
http://find/


262/824

A1, A2, . . . , An

i j Ai Aj

A1, A2, . . . , An

A1, A2, . . . , An A1 A2 An

A1 A2 An

Ai i 1, n

A1, A2, . . . , An A1 A2 An

A1A2 . . . An Ai i 1, n

A A A
http://find/


263/824

A1, A2, . . . , An

i j Ai Aj

A1

A2

A3
http://find/


264/824

n

A1, A2, . . . , An

P A1 A2 An P A1 P A2 P An
http://find/


265/824
http://find/


266/824

A B

A B P AB

A B
http://find/


267/824

35 10

15 6 4

P T C

19

15

P T C 15 19 0.789
http://find/


268/824

P T C 15 19 0.789

P T C 15 19 15 35

19 35

P T C

P C

35 10

15 6 4

P T C

19

15

P T C 15 19 0.789


269/824

P T C 15 19 15 35

19 35

P T C

P C

35 10

15 6 4

P T C

19

15

P T C 15 19 0.789
http://find/


270/824

P T C 15 19 15 35

19 35

P T C

P C

35 10

15 6 4

P T C

19

15

P T C 15 19 0.789
http://find/


271/824

P T C 15 19 15 35

19 35

P T C

P C

35 10

15 6 4

P T C

19

15

P T C 15 19 0.789
http://find/


272/824

P T C 15 19 15 35

19 35

P T C

P C

A B

P AB P

A

B

P B

P B 0

B A

AP A B
http://find/


273/824

P B A P A B

P A

P A 0

P AB

A B

P A B P AB P B

P B A P A
http://find/


274/824

1000

68.3%

62%

85%
http://find/


275/824

1000

68.3%

62%

85%
http://find/


276/824

1000

68.3%

62%

85%


277/824

1000

68.3%

62%

85%
http://find/


278/824

1000

C1

C2

S

V

P C1 0.683 P S 0.62 P C1 S 0.85

P C1 S P S P C1 S 0.62 0, 85 0.527

527 1000


279/824

1000

C1

C2

S

V

P C1 0.683 P S 0.62 P C1 S 0.85

P C1 S P S P C1 S 0.62 0, 85 0.527

527 1000


280/824

1000

C1

C2

S

V

P C1 0.683 P S 0.62 P C1 S 0.85

P C1 S P S P C1 S 0.62

0, 85

0.527

527 1000


281/824

1000

C1

C2

S

V

P C1 0.683 P S 0.62 P C1 S 0.85

P

C1

S

P

S

P

C1

S

0.62

0, 85

0.527

527 1000


282/824

1000

C1

C2

S

V

P C1 0.683 P S 0.62 P C1 S 0.85

P

C1

S

P

S

P

C1

S

0.62

0, 85

0.527

527 1000


283/824

S V

C1

C2


284/824

S V

C1

C2


285/824

A B

P AB P A P B A P B
http://find/


286/824

A B P A B P A P B


287/824

n

A1, A2, . . . , An

n

A1, A2, . . . , An

P A1A2 . . . An P A1 P A2 . . . P An
http://find/


288/824

3

0.01 0.02 0.03

Ai i i 1, 2, 3

A

A1A2A3

A1A2A3

A1A2A3

A1 A2 A3

P A P

A1A2A3 A1A2A3 A1A2A3

P A1A2A3 P A1A2A3 P A1A2A3

P A1 P A2 P A3 P A1 P A2 P A3

P A1 P A2 P A3
http://find/


289/824

1 2 3

0.99 0.02 0.03 0.01 0.98 0.03

0.01 0.02 0.97

0.0011

3

0.01 0.02 0.03

Ai i i 1, 2, 3

A

A1A2A3

A1A2A3

A1A2A3

A1 A2 A3

P A P

A1A2A3 A1A2A3 A1A2A3

P A1A2A3 P A1A2A3 P A1A2A3

P A1 P A2 P A3 P A1 P A2 P A3

P A1 P A2 P A3


290/824

1 2 3

0.99 0.02 0.03 0.01 0.98 0.03

0.01 0.02 0.97

0.0011

A1, A2. . . . , An

A1 A2 An

Ai Aj i j

A, A


291/824

Ai i A1, A2, A3

A1, A2. . . . , An H

P H

n

i 1

P HAi P Ai

P HA1 P A1 P HA2 P A2 P HAn P An
http://find/


292/824

A1, A2. . . . , An H A1, H A2, . . . , H An

H H H A1 H A2 H An

P

H

P

H

A1

H

A2

H

An

P H A1 P H A2 P H An

P H A P A P H A P A P H A P A
http://find/


293/824

http://find/


294/824

32%

Ai i i 1, 2

T

P T 0.32 P A1 P A2 0.5 P T A1 0.5

P T A2

A1 A2

P T P T A1 P A1 P T A2 P A2

0 5 0 5 P T A 0 5 0 32
http://find/


295/824

0.5 0.5 P T A2 0.5 0.32

P T A2 0.32 0.25 0.5 0.14

A1, A2, . . . , An H

i 1, n

P Ai H P HAi P Ai

P H

P HAi P Ai

http://find/


296/824

P HAi P Ai P Ai H P H

P

Ai

H

P HAi P Ai

P H

P H P HA1 P A1 P HA2 P A2 P HAn P An

P Ai H P HAi P Ai

P H A P A P H A P A P H A P A
http://find/


297/824

P Ai HP HA1 P A1 P HA2 P A2 P HAn P An

1

6

8

2 10 12

1

Ai

i

i

1, 2

X

P A1 X

P A1 H P

H

A1

P

A1

P HA1 P A1 P HA2 P A2

6 14 0 5
http://find/


298/824

6 14 0.5

6 14 0.5 10 22 0.5 0.485

1

6

8

2 10 12

1

Ai

i

i

1, 2

X

P A1 X

P A1 H P

H

A1

P

A1

P HA1 P A1 P HA2 P A2

6 14 0.5
http://find/


299/824

6 14 0.5

6 14 0.5 10 22 0.5 0.485
http://find/


300/824
http://find/


301/824

SS,SN,NS,NN
http://find/


302/824

X X

SS,SN,NS,NN
http://find/


303/824

X X

X

X
http://find/


304/824

X

X

X

X

X
http://find/


305/824
http://find/


306/824

X

X

X pX x p x

p x X
http://find/


307/824

X

X

X

X

p x
http://find/


308/824

X

P(x)

0.0

0.1

0.2

0.3

0.4

0.5
http://find/


309/824

X

0.5 0.0 0.5 1.0 1.5 2.0 2.5

0

0 p x 1

xp x 1


310/824

X X

X X X X

2X X
http://find/


311/824

X

x

x

xp x

X

2x

x

x X2p x

x

x2p x 2X

X X X

2
http://find/


312/824

X 2x

X

X

p x

X 1 0.2 0 0.1 3 0.6 4 0.1 2

2X 1 2

0.2 02 0.1 32 0.6 42 0.1 22 3.2
http://find/


313/824

f x

X X X

a, b

X a, b

P a X b

b

a

f x dx
http://find/


314/824

X x P X x 0

f x

X X X

a, b

X a, b

P a X b

b

a

f x dx


315/824

X x P X x 0

f x X

f x 0 x

f x 1
http://find/


316/824
http://find/


317/824
http://find/


318/824

n
http://find/


319/824

n

p

q 1 p
http://find/


320/824

X

X n

X

X B n, p x

n

P X x p x Cxnpxqn x n!

x! n x !pxqn x


321/824

3

0.51 X X

X B 3, 0.51

P X 2 3!

2!1!0.5120.491 0.382

P X 1 P X 1 P X 2 P X 3 0.88
http://find/


322/824

0 1 2 3 4 5

0.

0

0.

2

0.

4

0.

6

x

p(x)

PP nhi thuc voi n=5, p=0.1

0 1 2 3 4 5

0.

05

0.

15

0.

25

x

p(x)


0 1 2 3 4 5

0.

0

0.

2

0.

4

0.

6

x

p(x)


0 5 10 15 20

0.

00

0.

10

0.

20

p(x)


0 10 20 30 40 50

0.

00

0.

04

0.

08

p(x)

http://find/


323/824

x x

X X B n, p

X np, 2

X npq, X

npq
http://find/


324/824

X B n, p

P X x

P X x

x P X x
http://find/


325/824

X

x

P X x e

x

x!
http://find/


326/824

X

X P

X X P 5

P X 3 e 553

3! 0.14

Y Y P 2.5

2

P Y 2 1 P Y 0 P Y 1 0.712
http://find/


327/824

P Y 2 1 P Y 0 P Y 1 0.712

X X P 5

P X 3 e 553

3! 0.14

Y Y P 2.5

2

P Y 2 1 P Y 0 P Y 1 0.712
http://find/


328/824

0 0 7

0.0 1.0 2.0 3.0

0.

0

0.

2

0.

4

0.

6

0.

8

x

p(x)

PP Poisson voi trung binh 0.1

0 2 4 6 8 10

0.

0

0.

1

0.

2

0.

3

0.

4

0.

5

0.

6

x

p(x)

PP Poisson voi trung binh 0.5

0 2 4 6 8 10

0.

00

0.

10

0.

20

x

p(x)

PP Poisson voi trung binh 2

0 5 10 15

0.

00

0.

05

0.

10

0.

15

x

p(x)

PP Poisson voi trung binh 5
http://find/


329/824

X

X , 2

X , X
http://find/


330/824

X P

P X x

P X x

x P X x
http://find/


331/824

a b a b X

f x

1

b a a x b

0

X a, b X U a, b
http://find/


332/824

x

f(x)

a b

1

((b a))

c d

P(c


333/824

X a, b

X a b

2 , X

b a

12

P

c

X

d

d c

b a
http://find/


334/824

X

0 4

2.5

a 0 b 4 X

f x

1

4 0 x 4

0

2.5

P X 2.5 P 2.5 X 4 4 2.54 0

0.375
http://find/


335/824

X

0 4

2.5

a 0 b 4 X

f x

1

4 0 x 4

0

2.5

P X 2.5 P 2.5 X 4 4 2.54 0

0.375
http://find/


336/824

X U a, b

P X x

x P X x
http://find/


337/824

X

f x 1

2e

x 2

22

X X N , 2
http://find/


338/824

x

f((x))

1 2

Trung binh thay doi

x

f((x))

Phuong sai thay doi
http://find/


339/824

X X

a, b

x a x b

x

f((x))

a b

P(a


340/824

a b

X

Z X

0 1

0 1
http://find/


341/824

P a X b

P a X b

X N , 2

X N 6, 16 P 5 X 6.5

P 5 X 6.5 P 5 64

X 6

4

6.5 6

4 P 0.25 Z 0.13

P Z 0.13 P Z 0.25 Z N 0, 1

0.25 P Z 0.25 0.4

0.13

P

Z 0

.13 0

.552

P 5 X 6.5 0.552 0.4 0.152
http://find/


342/824

P a X b

P a X b

X N , 2

X N 6, 16 P 5 X 6.5

P 5 X 6.5 P 5 64

X 6

4

6.5 6

4 P 0.25 Z 0.13

P Z 0.13 P Z 0.25 Z N 0, 1

0.25 P Z 0.25 0.4

0.13

P

Z 0

.13 0

.552

P 5 X 6.5 0.552 0.4 0.152
http://find/


343/824

P a X b

P a X b

X N , 2

X N 6, 16 P 5 X 6.5

P 5 X 6.5 P 5 64

X 6

4

6.5 6

4 P 0.25 Z 0.13

P Z 0.13 P Z 0.25 Z N 0, 1

0.25 P Z 0.25 0.4

0.13

P

Z 0

.13 0

.552

P 5 X 6.5 0.552 0.4 0.152
http://find/


344/824

Z

P Z z P Z z

P Z 0 P Z 0 0.5

P Z z 0.5 P 0 Z z z

P Z z 0.5 P 0 Z z z
http://find/


345/824

X N , 2

P X x

x P X x
http://find/


346/824

X

f x

e x

x

00

X E

X

X 1

, X

1
http://find/


347/824

x

f(x)

=1 =4 =0.6
http://find/


348/824

X E

P X x 1 e x

P a X b e a e b
http://find/


349/824

f((x)) == e((x))

P(a


350/824

a b

1

2

X

X 1 1 2 0.5

P X 1 3 1 e1

3

0.5 1 e2 3 0.487
http://find/


351/824

1

2

X

X 1 1 2 0.5

P X 1 3 1 e1

3

0.5 1 e2 3 0.487
http://find/


352/824

1

2

X

X 1 1 2 0.5

P X 1 3 1 e1

3

0.5 1 e2 3 0.487
http://find/


353/824

X E

P X x

x P X x
http://find/


354/824
http://find/


355/824

X X B n, p n p

np 5 nq 5 q 1 p X

np

npq

X B 50, 0.5 P X 24

np 50 0.5 25 5 nq 50 0.5 25 5

X 25

50 0.5 0.5 3.536

P X 24 P 23.5 X 24.5

X P 23.5 X 24.5 P 23.5 25

3.536 Z

24.5 25

3.536 P 0.42 Z 0.14 0.11

P X 24 0.11
http://find/


356/824

P

20

X

30

P

21

X

30

P

20.5

X

30.5

P X 29 P 0.5 X 29.5

P X 35 P 36 X 50 P 35.5 X 50.5

P 18 X 42 P 19 X 41 P 18.5 X 41.5
http://find/


357/824

X

5 X

X 10

8

P

X

8

P

X

8.5

P

Z

8.5 10

10

0.318
http://find/


358/824

X

5 X

X 10

8

P

X

8

P

X

8.5

P

Z

8.5 10

10

0.318


359/824

X X

FX x FX x P X x

x

X p x

FX x P X x

t x

p t

X f x

FX x P X x

x

f t dt


360/824

X X

FX x FX x P X x

x

X p x

FX x P X x

t x

p t

X f x

FX x P X x

x

f t dt


361/824

Y X Y x

y

X

x

Y

y

X Y

a, b E aX b aEX b V aX b a2V X E X Y EX EY

V X Y V X V Y X Y
http://find/


362/824

Y X Y x

y

X

x

Y

y

X Y

a, b E aX b aEX b V aX b a2V X E X Y EX EY

V X Y V X V Y X Y
http://find/


363/824
http://find/


364/824
http://find/


365/824
http://find/


366/824
http://find/


367/824
http://find/


368/824

{

,

,

,

}

= +

+

+

= .
http://find/


369/824

=

+

+

.

+

+

.

+

.

= .
http://find/http://find/


370/824

Do thi tan suat cua tong the

x

18 19 20 21 22 23

0

.00

0.

05

0.

10

0.

15

0.

20

0.

25

Do thi tan suat cho tong the 6 trung binh mau

y

18 19 20 21 22 23

0

.00

0.

05

0.

10

0.

15

0.

20


371/824

/


372/824

=

=/

= /


373/824

Histogram of TongThe

TongThe

Density

0 1 2 3 4 5

0.0

0

0.0

5

0.1

0

0.1

5

0.2

0

Histogram of TrungBinhMau

TrungBinhMau

Density

2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.0

0.5

1.0

1.5

2.0


374/824

=

=

(

/ . = .

. = .
http://find/


494/824

: = : >

=

/

= .

. /

= .

= . . = . <

= .

.

= . > = .

. = . >

( >

) =

(

>

.

) =

.

>

.

=

.

>

. = .
http://find/


495/824

(

>

)

(

|

|)

=

/

Documents

Bài giảng Xác suất Thống kê và ứng dụng Tác giả: Phan Thanh Hồng, Trường Đại học Thăng Long, 2009