Tagged Questions
1
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0answers
13 views
Dimension free Concentration bounds for Martingales
Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$:
At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
1
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1answer
39 views
Inequality concerning the pairwise correlation coefficients of three random variables
I was asked to prove:
The correlation coefficients, $\rho_{12}$, $\rho_{23}$, $\rho_{13}$ between three random variables $X_1$, $X_2$, $X_3$ obey
...
0
votes
1answer
90 views
Covariance and Correlation
Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples.
Find:
a) E(X)
b) Var(X)
...
0
votes
1answer
36 views
Correlation of Indicator Variables
Show that for indicator random variables IA and IB of Events A and B:
Corr(IA, IB) = Corr(IAc, IBc) = -Corr(IA, IBc) = -Corr(IAc, IB)
Deduce that if A and B are positively dependent, then so are Ac ...
0
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0answers
39 views
Invariance of the correlation coefficient under linear transformations
Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign
= -Corr(X,Y) if a and c have opposite ...
0
votes
1answer
43 views
Is the relation of having positive covariance well behaved with respect to taking the inverse?
Let $X$ and $Y$ be two random variables, $X$ strictly positive. Assume that Cov$(X,Y)>0$. Does this imply that Cov$(1/X, Y)<0$?
I know that being positively correlated is not a transitive ...
3
votes
2answers
52 views
Covariance$(X,Y) \geq 0$ if $X,Y \geq 0$?
I was wondering if you can say something about the covariance of two positive variables $X$ and $Y$?
0
votes
1answer
27 views
Normal distribution $\rho_{X,Y} = 0 \rightarrow X \bot Y$
Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$.
Can someone give a hint why this is true ?
0
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1answer
52 views
correlation between two different variables
I am studying stochastic processes and found the next problem:
Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
0
votes
2answers
34 views
Correlation bound
Let x and y be two random variables such that:
Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
1
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0answers
18 views
Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.
I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
1
vote
3answers
479 views
Correlation between three variables question
I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple ...
3
votes
1answer
78 views
Autocorrelation of wrapped Wiener process
Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate
$$E(z(t)z(t+\tau)).$$
This is equal to ...
1
vote
1answer
100 views
Find correlation of x and y, given E(Y|X) and E(X|Y)
Suppose that X and Y are random variables such that E(Y | X) = 7 - (1/4)x and E(X | Y) = 10 - Y . Determine the correlation of X and Y .
Edit:
So far I've got
E(x)=4
E(y)=6
Now I'm trying to ...
1
vote
1answer
46 views
How can I show that $z_i =\cos(iw)$ where $w$ is uniform on $[0,2\pi]$ is a white noise process?
How can I show that $z_i =\cos(iw)$, where $w$ is uniform on $[0,2\pi]$ is a white noise process?
So far, I have shown $E(z_i)=0$ by integrating. However, I need to show ...
0
votes
2answers
84 views
Step by step correlation calculation
I must understand how I can calculate the correlation for the following probability variables.
...
1
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0answers
89 views
Windowed Linear Correlation
$\DeclareMathOperator \Cov {Cov}$
$\DeclareMathOperator \Var {Var}$
$\DeclareMathOperator \E {E}$
Consider the following experiment:
For $N\geq1$, consider $N$ black balls. Let us paint each black ...
2
votes
1answer
152 views
Necessary and sufficient conditions for a matrix to be a valid correlation matrix.
It's not too hard to see that any correlation matrix must have certain properties, such as all entries in the range -1 to 1, symmetric, positive semi-definite (excluding pathological cases like ...
0
votes
0answers
205 views
jointly stationary random process
If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is
$R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$,
which will be a constant, ...
0
votes
1answer
408 views
Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent)
Would like to know how to approach this question:
Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent).
Seen the solution for the ...
2
votes
2answers
65 views
Independence of Random Variables (kernel ICA)
In the paper
Bach, F. R., & Jordan, M. I. (2002). Kernel Independent Component
Analysis. Journal of Machine Learning Research, 3(1), 1-48.
doi:10.1162/153244303768966085
I stumpled upon ...
0
votes
0answers
39 views
Finding out whether or not two graphs are “close”, given 20 points on each graph whose Xs do not match
Let's assume we have two graphs where:
Each graph has 600 points per minute.
We're allowed to get only one point per minute.
We do not get the same point per minute in both graphs. So for example, ...
1
vote
1answer
85 views
In search of memorable example of “(Pearson-)uncorrelated $\not\Rightarrow$ independent”
I am looking for an easy-to-remember (and non-trivial) example that vividly illustrates that the "uncorrelatedness" (in the sense of Pearson) of two random variables $X, Y$ does not imply that $X$ and ...
3
votes
3answers
278 views
Correlation between variables
I asked this question on stats SE but did not find a suitable answer so far. Maybe someone can help.
Given n random variables x1,...,xn (one-dimensional).
The following is known (corr() = Pearson ...
1
vote
1answer
222 views
Expectation product of pairwise uncorrelated variables
Suppose I have three uncorrelated random variables $X, Y$ and $Z$ (discrete or continuous) such that
$$\newcommand{\Cov}{\mathrm{Cov}}\Cov(X,Y)=0;\quad \Cov(Y,Z)=0;\quad \Cov(X,Z)=0 \tag{$\ast$}$$
I ...
1
vote
3answers
128 views
correlated or independent
Let $(X_1, X_2)$ be a randomly chosen pair out of $\{1,2, \ldots, 20\}$ (draw without repetition).
Are both events $$E_1:=\{X_1 \geq 8\}$$ and $$E_2:=\{X_2 \geq 12\}$$ positive or negative correlated. ...
0
votes
1answer
187 views
indicator variable are uncorrelated, if they are independent?
Is it true that if two indicator variables are independent then they are uncorrelated?
If covariance =0 $\Rightarrow$ uncorrelated
Does the covariance between indicator variables exist?
thx
4
votes
3answers
406 views
Bounds on off-diagonal entries of a correlation matrix
Assume that all the entries of an $n \times n$ correlation matrix which are not on the main
diagonal are equal to $q$. Find upper and lower bounds on the possible values of $q$.
I know that the ...
1
vote
2answers
3k views
Calculating the variance of the ratio of random variables
I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is
$$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$
but, how do I derive it from "common" ...
1
vote
1answer
326 views
Correlation between Beta distributions
I have a Computer Science background and not very knowledgeable in Probability and Statistics. So excuse me if my question,notation, or language is flawed. Anyways, the problems is that we have two ...
