, .
1.
́ ́ .
- X {\displaystyle X} ,
P (X = x i) = p i, ∑ i = 1 ∞ p i = 1 {\displaystyle \mathbb {P} (X=x_{i})=p_{i},\;\sum \limits _{i=1}^{\infty }p_{i}=1}
:
M [ X ] = ∑ i = 1 ∞ x i p i {\displaystyle M[X]=\sum \limits _{i=1}^{\infty }x_{i}\,p_{i}}
- F X (x) {\displaystyle F_{X}(x)} , :
2.
́ ́ ́ , .
,
.
X {\displaystyle X} ,
D [ X ] = ∑ i = 1 n p i (x i − M [ X ]) 2 {\displaystyle D[X]=\sum _{i=1}^{n}{p_{i}(x_{i}-M[X])^{2}}}
X {\displaystyle X} , :
D [ X ] = ∫ − ∞ ∞ f (x) (x − M [ X ]) 2 d x {\displaystyle D[X]=\int _{-\infty }^{\infty }{f(x)(x-M[X])^{2}dx}}
( , ) :
.
, , .
3.
( ). :
.
: X Y .
( ). :
.
:
1. -1 +1.
2. 0.
3. , -1 +1.
x i {\displaystyle x_{i}} i - ; n {\displaystyle n} .
:
:
:
Excel:
: =()
: =()
: =()
: =( 1; 2)
3. , 1.
|
|
() ( ). :
.
: X Y .
( ). :
,
σ ( , ) :
.
:
1. -1 +1.
2. .
3. , -1 +1.
4. , , -1 +1. , , .
, .
x i {\displaystyle x_{i}}Xi Yi i - X Y ; n {\displaystyle n} .
:
, , , D .. :
D | ... | ||||
A | rAA=1 | rAB | rAC | rAD | ... |
B | r=1 | rBC | rBD | ... | |
C | r=1 | rCD | ... | ||
D | rDD=1 | ... | |||
... | ... | ... | ... | ... | ... |
:
1. 1, rAA=r= r=... =1 , , 1.
2. , .. rAB = rBA, , , .
4.
1. N=1000 : =10, s=3 N(10, 3).
2. B-E, 1000 :
1) B=2A+3,
2) =-3A+6,
3) D=5A+N(0, 15),
4) =N(2, 2)
5) F=(A-10)2.
N(, σ) σ.
10 .
, B, , D, F Excel:
: =( 1; 2)
.