- \
sigma _{X}^{2})}
Y ∼ N ( μ
Y , σ
Y 2 ) {\displaystyle
Y\sim N(\mu _{
Y},\
sigma _{
Y}^{2})} Z = X +
Y , {\displaystyle Z=X+
Y,} then Z ∼ N ( μ X + μ
Y ,...
- {\begin{aligned}\
sigma _{1}=\
sigma _{x}&={\begin{pmatrix}0&1\\1&0\end{pmatrix}},\\\
sigma _{2}=\
sigma _{
y}&={\begin{pmatrix}0&-i\\i&0\end{pmatrix}},\\\
sigma _{3}=\sigma...
-
generated by
Y {\displaystyle
Y} is σ (
Y ) = {
Y − 1 ( A ) : A ∈ σ ( F X ) } = σ ( {
Y − 1 ( A ) : A ∈ F X } ) , {\displaystyle \
sigma (
Y)=\left\{
Y^{-1}(A):A\in...
- {3A}{\
sigma _{X}\
sigma _{
Y}}}&0&0&{\frac {-1}{\
sigma _{
Y}}}&{\frac {-1}{\
sigma _{X}}}\\0&{\frac {\
sigma _{X}}{A\
sigma _{
Y}}}&0&0&0\\0&0&{\frac {\
sigma _{
Y}}{A\sigma...
- x σ x
y σ x z σ
y x σ
y y σ
y z σ z x σ z
y σ z z ] ≡ [ σ x τ x
y τ x z τ
y x σ
y τ
y z τ z x τ z
y σ z ] {\displaystyle {\boldsymbol {\
sigma...
- _{
Y}\end{pmatrix}},\quad {\boldsymbol {\
Sigma }}={\begin{pmatrix}\
sigma _{X}^{2}&\rho \
sigma _{X}\
sigma _{
Y}\\\rho \
sigma _{X}\
sigma _{
Y}&\
sigma _{
Y}^{2}\end{pmatrix}}...
- {\displaystyle \
sigma _{1}\neq 0,\
sigma _{3}=\
sigma _{2}=0} , the von
Mises criterion simply reduces to σ 1 = σ
y {\displaystyle \
sigma _{1}=\
sigma _{\text{
y}}\,\...
-
y 2 ( τ ) {\displaystyle \
sigma _{
y}^{2}(\tau )} . The
Allan deviation (ADEV), also
known as
sigma-tau, is the
square root of the
Allan variance, σ
y...
-
Y) \over \
sigma _{X}\
sigma _{
Y}}={\operatorname {E} [(X-\mu _{X})(
Y-\mu _{
Y})] \over \
sigma _{X}\
sigma _{
Y}},\quad {\text{if}}\ \
sigma _{X}\
sigma _{
Y}>0...
- = y r + i
y i {\displaystyle \
Sigma ={\begin{bmatrix}\
sigma _{x}^{2}&\rho \
sigma _{x}\
sigma _{
y}\\\rho ^{*}\
sigma _{x}\
sigma _{
y}&\
sigma _{
y}^{2}\end{bmatrix}}...
