binomial comparison graph
TRANSCRIPT
-
7/26/2019 Binomial Comparison Graph
1/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 0
, D2
A B
.@..
-
7/26/2019 Binomial Comparison Graph
2/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 1
CA 2: AD AAB AD ACAD C
1
1.1
1.2
1.3
2
2.1
2.2 :
2.3
2.4
: 2.5
2.6
-
7/26/2019 Binomial Comparison Graph
3/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 2
2.7
2.8
C
3
3.1
3.2
:
A
3.3 :
4 C
5
5.1
, A
5.2C ,
-
7/26/2019 Binomial Comparison Graph
4/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 3
5.3
6
6.1
6.2
6.3 :
7
7.1
7.2
7.3 C
7.4 C
7.5
-
7/26/2019 Binomial Comparison Graph
5/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 4
1
1.1
W
.S
o
o ;
o P
-
7/26/2019 Binomial Comparison Graph
6/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 5
1.2
S, .
F , M H
.
B, .
oF , M H
?
oH ?
oH I ?
T ,
-
7/26/2019 Binomial Comparison Graph
7/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 6
-
7/26/2019 Binomial Comparison Graph
8/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 7
W X ( Y, Z, )
X ( Y, Z,).
T (.., )
:
X. T
( )
-
7/26/2019 Binomial Comparison Graph
9/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 8
W (
X) , .. (
).
o ,
o
( ) ,
o ( )
I ,
,
.
W
-
7/26/2019 Binomial Comparison Graph
10/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 9
A
-
7/26/2019 Binomial Comparison Graph
11/97
-
7/26/2019 Binomial Comparison Graph
12/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 11
1.3
-
7/26/2019 Binomial Comparison Graph
13/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 12
-
7/26/2019 Binomial Comparison Graph
14/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 13
-
7/26/2019 Binomial Comparison Graph
15/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 14
-
7/26/2019 Binomial Comparison Graph
16/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 15
-
7/26/2019 Binomial Comparison Graph
17/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 16
-
7/26/2019 Binomial Comparison Graph
18/97
-
7/26/2019 Binomial Comparison Graph
19/97
-
7/26/2019 Binomial Comparison Graph
20/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 19
2
2.1
G X,
,
(CDF).
A , CDF , 1( )
N P(A), A ,
T
(PDF) ( ),
-
7/26/2019 Binomial Comparison Graph
21/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 20
(((10))) (((1000)))
-
7/26/2019 Binomial Comparison Graph
22/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 21
A, ANY F(.)
0,1
.
-
7/26/2019 Binomial Comparison Graph
23/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 22
2.2 :
-
7/26/2019 Binomial Comparison Graph
24/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 23
T
X,
X, .
-
7/26/2019 Binomial Comparison Graph
25/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 24
-
7/26/2019 Binomial Comparison Graph
26/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 25
T
;
:
T X
-
7/26/2019 Binomial Comparison Graph
27/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED
T
W
FUNCTIONS
.
2 26
CHAPTER 2 RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 27
-
7/26/2019 Binomial Comparison Graph
28/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 27
2.3
CHAPTER 2 RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 28
-
7/26/2019 Binomial Comparison Graph
29/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 28
B
-
7/26/2019 Binomial Comparison Graph
30/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 29
-
7/26/2019 Binomial Comparison Graph
31/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 31
-
7/26/2019 Binomial Comparison Graph
32/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 31
B P(X = )
. O , =100 =0.1,0.5. O , =0.5 =25,150
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 32
-
7/26/2019 Binomial Comparison Graph
33/97
2.4 :
F X, CDF
.
T X
X
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 33
-
7/26/2019 Binomial Comparison Graph
34/97
T
;
:
T X
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 34
-
7/26/2019 Binomial Comparison Graph
35/97
W ,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 35
-
7/26/2019 Binomial Comparison Graph
36/97
D
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 36
-
7/26/2019 Binomial Comparison Graph
37/97
2.5
I , ( )
.T "",
G :
( ) 2
( ).
T = 0 2= 1 .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 37
-
7/26/2019 Binomial Comparison Graph
38/97
D
. T .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 38
-
7/26/2019 Binomial Comparison Graph
39/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 39
-
7/26/2019 Binomial Comparison Graph
40/97
2.6 (= )
I CDF
U, , , . O
, , :
( = )
T CDF ( 0.5
).
T CDF
( ).
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 40
-
7/26/2019 Binomial Comparison Graph
41/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 41
-
7/26/2019 Binomial Comparison Graph
42/97
T I
R
(://../)
(=(1,2))
-
7/26/2019 Binomial Comparison Graph
43/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 43
-
7/26/2019 Binomial Comparison Graph
44/97
CD
I Y 0,1 F. T
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 44
-
7/26/2019 Binomial Comparison Graph
45/97
B , ( )
. T , 0.3 ( 30%) 30%
70% .
M , X
T
X:
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 45
-
7/26/2019 Binomial Comparison Graph
46/97
F, , X, ,
X (..,
N ).
S : , , , W
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 46
-
7/26/2019 Binomial Comparison Graph
47/97
2.7
T
P: S
3 , X
D X () 2 () 2 6 .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 47
-
7/26/2019 Binomial Comparison Graph
48/97
A CDF . F ():
F ():
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 48
-
7/26/2019 Binomial Comparison Graph
49/97
T X
N 1
H X
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 49
-
7/26/2019 Binomial Comparison Graph
50/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 50
-
7/26/2019 Binomial Comparison Graph
51/97
I :
F ,
,
,
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 51
-
7/26/2019 Binomial Comparison Graph
52/97
E
( )
, I
(: 10) .
W
10
, CDF
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 52
-
7/26/2019 Binomial Comparison Graph
53/97
2.8 C
I , , CDF,
. T CDF 1/
. T CDF .
T KS (KS)
(..
).
T 2 KS
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 53
-
7/26/2019 Binomial Comparison Graph
54/97
3
I
,
W X Y ,
,
J , X Y ,
.
A ,
,
( > 2)
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 54
3 1
-
7/26/2019 Binomial Comparison Graph
55/97
3.1
T X Y, ,
,
,
A ,
:
X Y, .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 55
A
-
7/26/2019 Binomial Comparison Graph
56/97
A,
,
X
Y
T
:
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 56
I X Y
-
7/26/2019 Binomial Comparison Graph
57/97
I X Y ,
, .
I 0 1 III I
Q I
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 57
I X Y
-
7/26/2019 Binomial Comparison Graph
58/97
I X Y ,
:
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED
I
FUNCTIONS
2 58
-
7/26/2019 Binomial Comparison Graph
59/97
I
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 59
C
-
7/26/2019 Binomial Comparison Graph
60/97
C
I ,
. C
.
T . T
.C
. T
,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 60
C
-
7/26/2019 Binomial Comparison Graph
61/97
C
. B ,
. T
:
N
W
. T
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 61
S'
-
7/26/2019 Binomial Comparison Graph
62/97
S
. S'
, C
.
T , , C
CDF.
T : ()
2
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 62
3.2 :
-
7/26/2019 Binomial Comparison Graph
63/97
3.2 :
L X Y , , = 1,2, ,
. T X Y
. I , , = 1,2, ,
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 63
A :
-
7/26/2019 Binomial Comparison Graph
64/97
A :
H, .
A,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 64
A
-
7/26/2019 Binomial Comparison Graph
65/97
I ,
( )
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 65
N,
-
7/26/2019 Binomial Comparison Graph
66/97
,
. E , (+=1) . W
.
Q: W
5 ?
A: W X
Y
5 .
oC,
oB
o
S,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 66
oI :
-
7/26/2019 Binomial Comparison Graph
67/97
C , 1 ( !)
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 67
F , :
-
7/26/2019 Binomial Comparison Graph
68/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 68
T
-
7/26/2019 Binomial Comparison Graph
69/97
( =0.4 =0.6):
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 69
3.3 :
-
7/26/2019 Binomial Comparison Graph
70/97
T 2 X Y
S ,
.
A :
X Y
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 70
A,
-
7/26/2019 Binomial Comparison Graph
71/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 71
-
7/26/2019 Binomial Comparison Graph
72/97
A 9 10, 10 . I
,
, .
A: X ,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 72
-
7/26/2019 Binomial Comparison Graph
73/97
T
. T .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 73
-
7/26/2019 Binomial Comparison Graph
74/97
W ,
,
F ,
2
0,60
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 74
4 C
-
7/26/2019 Binomial Comparison Graph
75/97
T
T X,
Y ,
W X ,
X Y=
F X, X
Y=
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 75
I , ,
-
7/26/2019 Binomial Comparison Graph
76/97
U ,
X Y ,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 76
T
-
7/26/2019 Binomial Comparison Graph
77/97
X, Y=, :
B
,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 77
F
-
7/26/2019 Binomial Comparison Graph
78/97
. B
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 78
W X Y , ,
-
7/26/2019 Binomial Comparison Graph
79/97
( ) (
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 79
F, X Y ,
-
7/26/2019 Binomial Comparison Graph
80/97
,
N
.
G ,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 80
-
7/26/2019 Binomial Comparison Graph
81/97
R R .
O
, R
(),
.
D
R ( :
4852 .
A:
A
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 81
W
-
7/26/2019 Binomial Comparison Graph
82/97
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 82
W
-
7/26/2019 Binomial Comparison Graph
83/97
.
T . W
N, . W
?
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 83
A:
-
7/26/2019 Binomial Comparison Graph
84/97
T . T
1/
1.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 84
5
-
7/26/2019 Binomial Comparison Graph
85/97
5.1
,
L (X) X. T
(X) E((X))
X X.
W 1 ,
; ,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 85
I X ,
-
7/26/2019 Binomial Comparison Graph
86/97
, ,
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 86
B E(.),
( ) ( )
-
7/26/2019 Binomial Comparison Graph
87/97
(X) (X) :
P . F , 3
:
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 87
L
-
7/26/2019 Binomial Comparison Graph
88/97
L ; , , X :
T , ,
X T :
oA X
o
A X
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 88
-
7/26/2019 Binomial Comparison Graph
89/97
F : ,
,
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 89
L T I
-
7/26/2019 Binomial Comparison Graph
90/97
L T . I T
( ):
T T ,
T. T ,
T E(T)
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 90
A
A
-
7/26/2019 Binomial Comparison Graph
91/97
A , 0 +1 1
.
T : A
. I ,
. I ,
. A , 1, 1, 3, 3,
5, 5. W , , ,
1. T 10 1 1 (
), 5 3 ( ), 5
3 ( ), 1 5
( ), 1 5 ( ).
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 91
-
7/26/2019 Binomial Comparison Graph
92/97
E 0. T ( )
( ).
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 92
S 5 .
-
7/26/2019 Binomial Comparison Graph
93/97
T ,
1 1 50% ,
. T
. T 1 1 ,
1.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 93
T 0. T ,
T
-
7/26/2019 Binomial Comparison Graph
94/97
. T :
.
A ,
.
T , ,
.
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 94
-
7/26/2019 Binomial Comparison Graph
95/97
S . H
?
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 95
T , , :
,
-
7/26/2019 Binomial Comparison Graph
96/97
. I ,
. T : ,
.
T :
, . T , , ,
0 .
CHAPTER 2: RANDOM VARIABLES AND ASSOCIATED FUNCTIONS 2 96
A , . A ,
:
1 1 A
-
7/26/2019 Binomial Comparison Graph
97/97
1 1. A ,
. I 1, 2
. I 1, 2 . S, ..
, 2.
I ,