Find correlation/covariance of two distributions with shared marginal distributions

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I have two distributions which represent the sum of smaller distributions.



Say distribution X is made up of distributions a, b and c: $mu_a$ = 10, $sigma_a$ = 3; $mu_b$ = 15, $sigma_b$ = 5; $mu_c$ = 20, $sigma_c$ = 4; so $mu_X$ = 45 and $sigma_X$ = $sqrt50$.



Distribution Y is made up of a, d and e: $mu_a$ = 10, $sigma_a$ = 3 (this is of course the same as the a above); $mu_d$ = 18, $sigma_d$ = 2; $mu_e$ = 12, $sigma_e$ = 4; so $mu_X$ = 40 and $sigma_X$ = $sqrt29$.



With this information, is there a way that I can find the correlation/covariance between the two distributions? Would it have to do with how much a contributes to X and Y's means and/or variances?




normal-distribution covariance correlation




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  • Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
    – Graham Kemp
    Aug 6 at 0:10











  • @GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
    – aaron
    Aug 6 at 0:13














up vote
0
down vote

favorite












I have two distributions which represent the sum of smaller distributions.



Say distribution X is made up of distributions a, b and c: $mu_a$ = 10, $sigma_a$ = 3; $mu_b$ = 15, $sigma_b$ = 5; $mu_c$ = 20, $sigma_c$ = 4; so $mu_X$ = 45 and $sigma_X$ = $sqrt50$.



Distribution Y is made up of a, d and e: $mu_a$ = 10, $sigma_a$ = 3 (this is of course the same as the a above); $mu_d$ = 18, $sigma_d$ = 2; $mu_e$ = 12, $sigma_e$ = 4; so $mu_X$ = 40 and $sigma_X$ = $sqrt29$.



With this information, is there a way that I can find the correlation/covariance between the two distributions? Would it have to do with how much a contributes to X and Y's means and/or variances?




normal-distribution covariance correlation




share|cite|improve this question





















  • Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
    – Graham Kemp
    Aug 6 at 0:10











  • @GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
    – aaron
    Aug 6 at 0:13












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have two distributions which represent the sum of smaller distributions.



Say distribution X is made up of distributions a, b and c: $mu_a$ = 10, $sigma_a$ = 3; $mu_b$ = 15, $sigma_b$ = 5; $mu_c$ = 20, $sigma_c$ = 4; so $mu_X$ = 45 and $sigma_X$ = $sqrt50$.



Distribution Y is made up of a, d and e: $mu_a$ = 10, $sigma_a$ = 3 (this is of course the same as the a above); $mu_d$ = 18, $sigma_d$ = 2; $mu_e$ = 12, $sigma_e$ = 4; so $mu_X$ = 40 and $sigma_X$ = $sqrt29$.



With this information, is there a way that I can find the correlation/covariance between the two distributions? Would it have to do with how much a contributes to X and Y's means and/or variances?




normal-distribution covariance correlation




share|cite|improve this question













I have two distributions which represent the sum of smaller distributions.



Say distribution X is made up of distributions a, b and c: $mu_a$ = 10, $sigma_a$ = 3; $mu_b$ = 15, $sigma_b$ = 5; $mu_c$ = 20, $sigma_c$ = 4; so $mu_X$ = 45 and $sigma_X$ = $sqrt50$.



Distribution Y is made up of a, d and e: $mu_a$ = 10, $sigma_a$ = 3 (this is of course the same as the a above); $mu_d$ = 18, $sigma_d$ = 2; $mu_e$ = 12, $sigma_e$ = 4; so $mu_X$ = 40 and $sigma_X$ = $sqrt29$.



With this information, is there a way that I can find the correlation/covariance between the two distributions? Would it have to do with how much a contributes to X and Y's means and/or variances?





normal-distribution covariance correlation





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 9 at 14:48









TZakrevskiy

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19.8k12253









asked Aug 6 at 0:02









aaron

62




62











  • Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
    – Graham Kemp
    Aug 6 at 0:10











  • @GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
    – aaron
    Aug 6 at 0:13
















  • Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
    – Graham Kemp
    Aug 6 at 0:10











  • @GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
    – aaron
    Aug 6 at 0:13















Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
– Graham Kemp
Aug 6 at 0:10





Only by knowing how $a,b,c,d,e$ are correlated. In textbook problems they are usually asserted to be pairwise independent; are they here?
– Graham Kemp
Aug 6 at 0:10













@GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
– aaron
Aug 6 at 0:13




@GrahamKemp I intended for them to be independent, although it would be interesting to see how the answer would change if a and b or any of my example variables were correlated.
– aaron
Aug 6 at 0:13















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