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I want to know Covariance of random variable between $X$ and $Y$ when $X$ is a F-distribution with degree of freedom $a$ and $b$ and $Y$ is a F-distribution with degree of freedom $c$ and $d$,in case $X$ and $Y$ are not independent.

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    $\begingroup$ What is the joint pdf of $X$ and $Y$? Absent that, how long is a piece of string. $\endgroup$
    – wolfies
    Commented Jul 4, 2018 at 6:29
  • $\begingroup$ Dear wolfies, In case, X and Y are independent random variable. I know joint pdf of X and Y. But in this case, X and Y are not independent, So I can not know joint pdf of X and Y. $\endgroup$
    – Itee Louis
    Commented Jul 4, 2018 at 7:37
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    $\begingroup$ ??????????????? $\endgroup$
    – wolfies
    Commented Jul 4, 2018 at 7:54
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    $\begingroup$ The covariance cannot be determined from this information. Presumably in the case you are interested in, you know something more about the dependence than just "not independent" - it might be helpful to explain how these distributions arise $\endgroup$
    – Juho Kokkala
    Commented Jul 4, 2018 at 12:04
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    $\begingroup$ This may help: stats.stackexchange.com/editing-help#LaTeX (though based on a quick glance I think the question itself is somewhat unclear - how do the "sample covariance matrices" arise or how they are related to the random vectors $\mathbf{X}_1$ and $\mathbf{X}_2$? $\endgroup$
    – Juho Kokkala
    Commented Jul 5, 2018 at 11:08

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