Tagged Questions
1
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1answer
36 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
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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 ...
0
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1answer
44 views
What is the correlation function in multivariable/vectoral case?
I know that the correlation function between random variables $X$ and $Y$ is defined as
$$
\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over ...
0
votes
1answer
52 views
correlation between two different variables
I am studying stochastic processes and found the next problem:
Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
0
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0answers
28 views
how to compare correlation between random variables?
Suppose I have a random variable, S(k) for starting date of callable bonds, M(k) for the maturity date of the bonds, and C(k) for the called date of the bonds.
$$S(k) < C(k) < M(k)$$
C(k) is ...
1
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0answers
18 views
Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.
I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
0
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0answers
33 views
Correlation Coefficient dealing with discretely distributed variables
I'm a bit stuck on this practice problem I have for my HS business stats class. I'd appreciate any help to get the solutions. Thank you.
Exercise #22: Let X and Y be discretely distributed random ...
1
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3answers
467 views
Correlation between three variables question
I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple ...
3
votes
1answer
78 views
Autocorrelation of wrapped Wiener process
Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate
$$E(z(t)z(t+\tau)).$$
This is equal to ...
1
vote
1answer
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
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0answers
50 views
Min and Max Correlation values
i want to know whats is the max value that the correlation rho can take :
$\mbox{Rho}(u_1,u_2) = \mbox{Cov}(u_1,u_2)/(\sigma_1*\sigma_2)$
where $u_1$ is a uniform random Variable and $u_2$ is an ...
