Variable aleatory multiple
Variable braces of aleatory
1) Function of combined cumulative distribution :
FXY (x,y) = P{X £ x, Y £ y} you notice yourself that se x = y = ¥ FXY (¥,¥) = 1
2) Function of combined cumulative density:
Positive function is like always the derivative of the
function
of distribution to the usual is one.
3) Function of marginal distribution :
It is obtained from the function of combined cumulative distribution saturating one of the 2 variable ones that is placing like ¥ one of the 2 ends, that one of x or the that one of the y.
4) Mass of combined probability :
It is used in the case that X and Y is 2 variable aleatory discreet P{X = xthe , Y = y } = pik the .
5) variable Condition of 2 independence of aleatory X and Y :
Two variable aleatory X and Y says statistically independent if the events {X £ x} e { Y £ are independent y}
6) Density of probability to circular symmetry :
A probability density f(x, y) is said to circular symmetry if it only depends on the distance of point x, y from the origin.
Variable function of one brace of aleatory
7) variable Function of one brace of aleatory
It is variable aleatory that it is obtained giving to the function g like input variable aleatory the X and the Y.
8) Expected value of one brace of variable aleatory :
9) Covarianza :
Cov(X, Y) = mXY = E{(X - hX) (Y - hY)}
10) Coefficient of correlation :
such
coefficient is in smaller module of 1, in particular it is worth 1 if
the points very are distributed around to one straight.
11) Variable aleatory scorrelate :
2 variable aleatory ones say scorrelate or incorrelate if E{XY} = E{X}E{Y} = hX hY , replacing in the respective definitions is had that 2 variable aleatory ones scorrelate have null covarianza and coefficient of null correlation also it.
In short 2 variable ones are scorrelate if they are lacking in a whichever linear tie.
12) scorrelate Variance of the sum of 2 variable ones :
13) Relation between independence and scorrelationship :
Two variable aleatory independent ones also are scorrelate but it is not said that 2 variable aleatory ones scorrelate are necessarily independent.
14) Straight of regression :
Draft of one straight having the scope to approximate one
second distribution a some model which as an example the linear model,
the straight one of regression of Y on X è :
.
15) Moments kinsmen :
mKR = E{XKYR}
16) combined characteristic Function :
You notice yourself that if X and Y is variable aleatory
independent 
17) regarding Theorem the transformation of one brace of variable aleatory :
If Z = g(X, Y) e W = h(X, Y)
18) Variable jointly Gaussian :
Two variable aleatory ones are jointly Gaussian if their
combined density is worth 
with 
and
Q(x, y) = c1x2 c2xy c3y2 c4x c5y c6 ³ 0
Conditioned distribution
19) variable conditioned Distribution of aleatory the X:
20) conditioned Density of 2 variable aleatory ones:
21) conditioned Expected value:
22) Principle of ortogonalità:
The error and = Y - j(x) is orthogonal to one generic function q(x)
Theory of the reliability
23) Life of a system:
It is the temporal interval that goes from the moment of activation of the same system until to the moment in which out of order it therefore FX(t) is the out of order probability that the system before the moment t.
24) Reliability of the system:
R(t) = 1 - FX(t) = P{X > t} therefore R(t) is the probability that the system functions to the moment t.
25) MTBF:
It is the mean time between failures, coincides with the
valor medium l of life X
26) conditioned Frequency of breakdowns b(t) :
27) Which are the possible courses of b(t) :
to) constant
b) with mortality infantile it is resolved with burn-in regarding the single members
c) with usury or invecchiamento is resolved with the programmed maintenance
d) to bathtub from bagno it is the sum of the effects of infantile mortality and usury
Variable sequences of aleatory
28) combined Distribution of N variable aleatory :
F(x1 ...., xN) = P{X1 £ x1 ....., XN £ xN }
from it they can be obtained the density combined of some variable ones replacing ¥ in remaining.
29) Matrix of covarianza :
Draft of one symmetrical matrix having in every intersection line - column the covarianza of respective the variable ones.
30) Measure of Gaussian probability on the N-dimensional space "n :
It is the measure that the exponential of a quadratic shape admits like density function.
31) Density multivaried of n variable aleatory independent :
Density is given simply from the product of the N Gaussian.
32) Gaussian aleatory Carrier :
Draft of that aleatory carrier for which whichever linear combination V of its members is one variable aleatory Gaussian, for every chosen of the coefficients.
Aleatory champion
33) aleatory Champion :
They are the N variable aleatory constructed to leave from variable aleatory the X.
34) Average of champion :
Draft of the average aritmetica 
Theorem of the limit centers them
35) typical Formulation :
Independent aleatory variable N dates, the theorem of the limit centers asserts them that the distribution of their sum approximates a normal distribution to growing of N. If variable the aleatory ones are continuous then the density of their sum approximate one normal density.
36) classic Formulation :
Independent aleatory N dates variable and identically
distributed, with valor medium h and ended variances 2, to stretching of N to variable ¥ the aleatory one 
stretch to one Gaussian standard N(0,1).
37) Formulation in terms of convoluzione :
The convoluzione of a great number of positive functions is approximately one normal curve
Convergence
38) stocastico Process :
Infinite sequence of variable aleatory X is one1 , X2 ...., XN .
39) Convergence nearly ovunque :
Of variable the aleatory ones they say to nearly converge ovunque if the limit of Xn(x) exists for all turns out to you which have not null probability.
40) quadratic Convergence in average :
The aleatory sequence XN is said to converge in average quadratic to c if 
41) Convergence in probability :
The aleatory sequence XN is said to converge in probability to c if 
every for and > 0.
42) Convergence in distribution :
The aleatory sequence XN says to converge in distribution if said Fn(x) = P{Xn £ x}le variable distributions of the
aleatory ones has 
.
43) Relation between the convergences :
Se a sequence converges in average quadratic converges in probability converges in distribution.