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independency

independency (ɪndɪˈpɛndənsɪ) Also 7–8 -ancy. [f. as prec. + -ency.] 1. = prec. 1. Now rare.1611 Florio, Independenza, independencie. 1645 H. Marten (title) The Independency of England Maintained against the Scottish Commissioners. 1646 Sir T. Browne Pseud. Ep. i. iii. 12 The independency of their ca... Oxford English Dictionary

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An appendix to The history of independency being a brief ...

... Clement Walker - An appendix to The history of ... Clement Walker The Exile|William Oxley Battlesystem ... de langue fran?aise. ? l'usage des classes inf ...

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Linear independency implies linear independence of the gradients Consider a set of linear independent and homogeneous polynomials $f_i:\mathbb{R}^n \rightarrow \mathbb{R}$ $i =1,\cdots,m$ and $m \leq n $. I wonder i...

This is of course false if we allow the polynomials to be constant, because the gradient of a constant is zero and thus linear dependent. But if we assume that all polynomials have positive degree, it is true as the following proof shows: In characteristic zero, the gradient of a polynomial is zero ...

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Independency of X,Y given that $X^2$, $Y^2$ are independent. Let $X$, $Y$ be random variables with positive probability density on every real number $x$. ($pdf_X(x)>0$, $pdf_Y(x)>0$ for every real $x$) If $X^2$ and ...

Let $W$ be a fair coin flip, and let $Z_1$ and $Z_2$ be independent standard normal random variables. If $W$ is heads, let $X=|Z_1|$ and $Y=|Z_2|$. Otherwise if $W$ is tails, let $X=-|Z_1|$ and $Y=-|Z_2|$. Then $X^2=Z_1^2$ and $Y^2=Z_2^2$ are independent because $Z_1$ and $Z_2$ are. However, $X$ and...

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Linearly Independency of functions Show if the functions are linearly independent $x(t)=3$, $y(t)=3\sin^2t$, $z(t)= 4\cos^2t$ How can i show this?

Can you compute the Wronskian?

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How to prove that the linear independency of $f_{i}$ from $C^{n-1}\left [ a, b \right ]$ to $C\left [ a, b \right ]$ How to prove that > if $f_{1}, f_{2}, ..., f_{n}$ are linearly independent in $C^{n-1}\left [ a, b ...

The inclusion $$I:C^{n-1}[a,b]\to C[a,b]$$ tautologically defined by $I(f)=f$ is a linear map which is injective. Therefore if $$C[a,b]\ni 0=\sum\lambda_i f_i=\sum\lambda_iI(f_i)=I(\sum\lambda_if_i)$$ we must have $\sum\lambda_if_i=0\in C^{n-1}[a,b]$. If $f_i$ are linearly independent on $C^{n-1}[a,...

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Question about independency of random variables let X, Y, Z be 3 random variables. if X and Y are independent and X and Z are independent, is X and (Y,Z) also independent? (if $$P(X \in A, Y \in B) =P(X \in A)P(Y\i...

No. See, for example, this answer for a simple example (in which $Y$ and $Z$ also are independent), that is, $X, Y, Z$ are _pairwise_ independent but not mutually independent, and so $X$ is not independent of the bivariate random variable $(Y,Z)$.

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If conditional expectation is a constant, can we infer the independency? If $E[Y\mid X]= c$ where $c$ is the same constant for any $X=x$ (actually it's just $c = EY$), can we say that $X$, $Y$ are independent?

No, otherwise the concept of martingale would not go beyond sums of independent random variables. Let us give an example: if $Y=\varepsilon X$, where $\varepsilon$ is zero-mean and independent of $X$, we have $\mathbb E\left[Y\mid X\right]=X\mathbb E\left[\varepsilon\right]=0$. In general, $\varepsi...

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Does the independency of $x_i|\theta$ implies the independency of $x_i$? Suppose we have a random sample $x_1, \cdots, x_n$ draw from the density $f(x|\theta)$ where $\theta$ is the parameter. If we know $x_i|\theta$ ...

Definitely not. Suppose that _conditioned on $\theta \in (0,1)$_ the $x_i$ are [conditionally] i.i.d. from $\text{Bernoulli}(\theta)$. Then $P(x_1=x_2=1) = E[\theta^2]$ while $P(x_1=1)P(x_2=1) = E[\theta]^2$. Thus $x_1$ and $x_2$ are marginally independent only if $\theta$ is a degenerate (constant)...

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Criterion for independency of random variables I saw in some notes the following "criterion" for independency of two random variables. Let $X$ and $Y$ be real-valued random variables defined on the same space. $X$ an...

1. "Any two functions" means Borel measurable functions (we need to integrate random variables) for which the integrals make sense (for example bounded functions). It's enough to do the test among $g$ and $h$ continuous bounded functions. Indeed, we can approximate pointwise the characteristic funct...

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linear independency for homogenous second order I can't figure out if this set of equations are linear independent or linear dependent. $$\\{\sin(t)+2\cos(t), \sin(t)-2\cos(t), 2\sin(t)+\cos(t), 2\sin(t)-\cos(t)\\}$$...

$(\sin(t)+2\cos(t)) + (\sin(t)-2\cos(t)) -\frac{1}{2}(2\sin(t) + \cos(t))-\frac{1}{2}(2\sin(t) - \cos(t))=0$

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Conditional Probability Independency Table Thinking A have found an alternative definition of independency for a given conditional probability $P(A|B)$, they are independent, iff all columns of the probability table a...

It means that $P(A=i\mid B=j)=P(A=i\mid B=k)$ for every $i$, $j$ and $k$.

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Trouble understanding the proof for linear independency of a basis for a linear transformation I am reading Matrix Analysis and Applied Linear Algebra by Meyer and the following statement and proof are given !enter im...

The author is proving that for $\sum_{j,i}\eta_{j,i}\mathbf B_{j,i}=0$ to hold, all $nm$ coefficients $\eta_{j,i}$ have to be zero, since that is the definition of linear independence. This is shown in groups of $m$ coefficients at a time, namely for fixed $k\in\\{1,\ldots,n\\}$ it is shown that $\e...

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How to show linear independency of non-zero vectors of a 3x3 matrix? If $C$ is a $3×3$ matrix and if the non-zero vectors $u$ and $v\in \Bbb R^3$ are such that, $Cu=2u$ and $Cv=−5v$ How can you show that $u$ and $v...

Suppose it is dependent. Then $$u=kv$$ where $k$ is non zero. Then $$Cu=kCv \implies 2u=-5kv$$ Now multiply $2$ on both sides of $u=kv$. Then we have $$2u=2kv$$ Subtract the two equations, we get $$0=7kv$$ and so $k=0$, a contradiction!

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Expected value inequality with zero-mean variable Let $X,Y$ be independent real valued random variables. In addition $\mathbb{E}[Y] = 0$ and $p\geq 1$. Then $$ \mathbb{E}[ |X|^p] \leq \mathbb{E}[ |X+Y|^p] $$ How can I...

\begin{align*} E|X+Y|^{p}&=\int_{{\bf{R}}\times{\bf{R}}}|u+v|^{p}d\mu_{(X,Y)}(u,v)\\\ &=\int_{{\bf{R}}\times{\bf{R}}}|u+v|^{p}d\mu_{Y}(v)d\mu_{X}(u)\\\ &\geq\int_{{\bf{R}}}\left|\int_{{\bf{R}}}vd\mu_{Y}(v)+u\right|^{p}d\mu_{X}(u)\\\ &=\int_{{\bf{R}}}\left|E(Y)+u\right|^{p}d\mu_{X}(u)\\\ &=\int_{{\bf...

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independency

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independency

An appendix to The history of independency being a brief ...

Linear independency implies linear independence of the gradients Consider a set of linear independent and homogeneous polynomials $f_i:\mathbb{R}^n \rightarrow \mathbb{R}$ $i =1,\cdots,m$ and $m \leq n $. I wonder i...

Independency of X,Y given that $X^2$, $Y^2$ are independent. Let $X$, $Y$ be random variables with positive probability density on every real number $x$. ($pdf_X(x)>0$, $pdf_Y(x)>0$ for every real $x$) If $X^2$ and ...

Linearly Independency of functions Show if the functions are linearly independent $x(t)=3$, $y(t)=3\sin^2t$, $z(t)= 4\cos^2t$ How can i show this?

How to prove that the linear independency of $f_{i}$ from $C^{n-1}\left [ a, b \right ]$ to $C\left [ a, b \right ]$ How to prove that > if $f_{1}, f_{2}, ..., f_{n}$ are linearly independent in $C^{n-1}\left [ a, b ...

Question about independency of random variables let X, Y, Z be 3 random variables. if X and Y are independent and X and Z are independent, is X and (Y,Z) also independent? (if $$P(X \in A, Y \in B) =P(X \in A)P(Y\i...

If conditional expectation is a constant, can we infer the independency? If $E[Y\mid X]= c$ where $c$ is the same constant for any $X=x$ (actually it's just $c = EY$), can we say that $X$, $Y$ are independent?

Does the independency of $x_i|\theta$ implies the independency of $x_i$? Suppose we have a random sample $x_1, \cdots, x_n$ draw from the density $f(x|\theta)$ where $\theta$ is the parameter. If we know $x_i|\theta$ ...

Criterion for independency of random variables I saw in some notes the following "criterion" for independency of two random variables. Let $X$ and $Y$ be real-valued random variables defined on the same space. $X$ an...

linear independency for homogenous second order I can't figure out if this set of equations are linear independent or linear dependent. $$\\{\sin(t)+2\cos(t), \sin(t)-2\cos(t), 2\sin(t)+\cos(t), 2\sin(t)-\cos(t)\\}$$...

Conditional Probability Independency Table Thinking A have found an alternative definition of independency for a given conditional probability $P(A|B)$, they are independent, iff all columns of the probability table a...

Trouble understanding the proof for linear independency of a basis for a linear transformation I am reading Matrix Analysis and Applied Linear Algebra by Meyer and the following statement and proof are given !enter im...

How to show linear independency of non-zero vectors of a 3x3 matrix? If $C$ is a $3×3$ matrix and if the non-zero vectors $u$ and $v\in \Bbb R^3$ are such that, $Cu=2u$ and $Cv=−5v$ How can you show that $u$ and $v...

Expected value inequality with zero-mean variable Let $X,Y$ be independent real valued random variables. In addition $\mathbb{E}[Y] = 0$ and $p\geq 1$. Then $$ \mathbb{E}[ |X|^p] \leq \mathbb{E}[ |X+Y|^p] $$ How can I...