Lets say that X is a normally distributed random variable with $\sigma_X = \lim_{a\to\infty} a$ and $E[X] = 0$. Lets say that Y is a normally distributed random variable with $\sigma_Y = \lim_{a\to\infty} 1/a$ and $E[Y] = 0$. What is the joint distribution covariance matrix of X and Y.
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$\begingroup$ Could you explain what does it mean $\lim_{a \rightarrow \infty}a$? $\endgroup$– echzhenFeb 29, 2016 at 22:22
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$\begingroup$ I just mean that the standard deviation of x is infinity and the standard deviation of y is 0. Since that is ambiguous I am saying that the standard deviation of x is approaching infinity and the standard deviation of y is approaching the reciprocal of that at the same rate. $\endgroup$– Sam BakerFeb 29, 2016 at 22:29
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$\begingroup$ but what is a normal distribution with standard deviation equals to infinity? Probably you should fix your notation to something like this: Given $X_n$ is a sequence of independent normally distributed variables with $\sigma_n$, s.t. $\lim_{n \rightarrow \infty}\sigma_n = \infty$... $\endgroup$– echzhenFeb 29, 2016 at 22:34
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$\begingroup$ No, X and Y are just scalar normal random variables. The covariance matrix is 2 by 2 with $/Sigma_X^2$ and $/Sigma_Y^2$ on the diagonals. I just need to know the correlation coefficient to make the covariance matrix. $\endgroup$– Sam BakerFeb 29, 2016 at 22:47
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$\begingroup$ There is no such thing as normal variable with $\sigma = \infty$. $\endgroup$– echzhenFeb 29, 2016 at 22:49
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