Joint distribution of two normal variables
0
$begingroup$
X and Y are independent random variables and they are represented as linear combination of two normal random variables. X=aW+bM and Y=cW+dM How do I compute the joint distribution of W and M?
Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution? Or will this approach fail as W and M might be corelated?
normal-distribution
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
$endgroup$
|
show 1 more comment
0
$begingroup$
X and Y are independent random variables and they are represented as linear combination of two normal random variables. X=aW+bM and Y=cW+dM How do I compute the joint distribution of W and M?
Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution? Or will this approach fail as W and M might be corelated?
normal-distribution
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
$endgroup$
$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14
|
show 1 more comment
0
0
0
$begingroup$
X and Y are independent random variables and they are represented as linear combination of two normal random variables. X=aW+bM and Y=cW+dM How do I compute the joint distribution of W and M?
Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution? Or will this approach fail as W and M might be corelated?
normal-distribution
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
$endgroup$
X and Y are independent random variables and they are represented as linear combination of two normal random variables. X=aW+bM and Y=cW+dM How do I compute the joint distribution of W and M?
Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution? Or will this approach fail as W and M might be corelated?
normal-distribution
normal-distribution
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
asked Dec 15 '18 at 6:35
AnalystAnalyst
1
1
$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14
|
show 1 more comment
$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14
$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14
|
show 1 more comment
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$begingroup$
"Can I rearrange the equations to represent W and M in terms of X and Y and then proceed to find the joint distribution?" Definitely the way to go. "Or will this approach fail as W and M might be corelated?" Is this supposed to be a reason why the approach should fail?
$endgroup$
– Did
Dec 15 '18 at 6:55
$begingroup$
I feel like of W and M are corelated then we cannot rearrange the equations like how we would normally do so while delaing with independent normal random variables. Because for independent random variables we can simply add their individual means and standard deviations but the same cannot be done for normal variables that are corelated
$endgroup$
– Analyst
Dec 17 '18 at 0:04
$begingroup$
You can rearrange the relations between random variables, of course, and then deduce from these relations the values of the moments you are interested in. Did you write down W and M in terms of X and Y?
$endgroup$
– Did
Dec 17 '18 at 0:08
$begingroup$
Yes that's how I proceeded. I wrote down W and M in terms of X and Y and found the variance and covariance of W and M.
$endgroup$
– Analyst
Dec 17 '18 at 0:12
$begingroup$
Thus, problem solved?
$endgroup$
– Did
Dec 17 '18 at 0:14