: .
. , X, () . , X , , .
■ - , ( , ), , . , . , , x, x . , 1, 2, 3, 4, 5, 6 . , ( , , ), (a; b).
■ , , . .
■ , . .
, , ; , , , .
, .. xi pi, . ( ), ( ) .
X x1, x2, , xn p1, p2, , pn, .. P(X=x1) = p1, P(X=x2) = p2, , P(X=xn) = pn. x1, x2, , xn,
X | x1 | x2 | xn | |
p | p1 | p2 | pn |
X , X=x1, X=x2, , X=xn , , , , .. p1 + p2 + + pn =1.
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. () .
, , . (X, Y, Z), (x, y, z). () .
, () .
, . .
1. :
xi | x1 | x2 | x3 | ... | xn |
pi | p1 | p2 | p3 | ... | pn |
X = xi (i = 1, 2, 3,,n) , .. . : 1+2+3++n = ∑pi =1
2. () P(X = xi) = ϕ(xi). :
) : Pn(X=k) = nk pk qn-k, 0<<1, k = 0, 1, 2, , n;
) :
λ>0, k = 0, 1, 2, .
) F(x), x , X , x, .. F(x) = P(X < x).
- F(x)
3. () ( 3).
, . , . , , , . .
:
- M ( ) M(X)=Σ xipi.
M(X)=np, M(X)=λ - D(X)= M[XM(X)]2 D(X) = M(X2)−[M(X)]2. XM(X) .
D(X)=npq, D(X)=λ - ( ) σ(X)=√D(X).
. , .
( ) , . , ( ) . ( ) . , . , .
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[26], , , ( ) ( ). , , ( ). , ( ) ( ), , ( ).