Marginal distribiution of X and Y
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"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent. "
I was thinking about something like this,
$$fx(x)=int_0.5^0.5 2;mathrmdy=2$$
but the proper answer is supposed to be one(for X and Y).
probability marginal-distribution
asked Sep 10 at 7:12
Adam Stawarek
61
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up vote
1
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favorite
"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent. "
I was thinking about something like this,
$$fx(x)=int_0.5^0.5 2;mathrmdy=2$$
but the proper answer is supposed to be one(for X and Y).
probability marginal-distribution
asked Sep 10 at 7:12
Adam Stawarek
61
3
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent. "
I was thinking about something like this,
$$fx(x)=int_0.5^0.5 2;mathrmdy=2$$
but the proper answer is supposed to be one(for X and Y).
probability marginal-distribution
asked Sep 10 at 7:12
Adam Stawarek
61
"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent. "
I was thinking about something like this,
$$fx(x)=int_0.5^0.5 2;mathrmdy=2$$
but the proper answer is supposed to be one(for X and Y).
probability marginal-distribution
probability marginal-distribution
asked Sep 10 at 7:12
Adam Stawarek
61
asked Sep 10 at 7:12
Adam Stawarek
61
asked Sep 10 at 7:12
Adam Stawarek
61
asked Sep 10 at 7:12
Adam Stawarek
61
asked Sep 10 at 7:12
Adam Stawarek
61
61
3
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17
add a comment |Â
3
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17
3
3
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17
add a comment |Â
1 Answer
1
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0
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Hints:
$$f_X(x)=int f_X,Y(x,y)dytext and f_Y(y)=int f_X,Y(x,y)dx$$
If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.
answered Sep 10 at 7:47
drhab
89.4k541123
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Hints:
$$f_X(x)=int f_X,Y(x,y)dytext and f_Y(y)=int f_X,Y(x,y)dx$$
If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.
answered Sep 10 at 7:47
drhab
89.4k541123
add a comment |Â
up vote
0
down vote
Hints:
$$f_X(x)=int f_X,Y(x,y)dytext and f_Y(y)=int f_X,Y(x,y)dx$$
If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.
answered Sep 10 at 7:47
drhab
89.4k541123
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Hints:
$$f_X(x)=int f_X,Y(x,y)dytext and f_Y(y)=int f_X,Y(x,y)dx$$
If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.
answered Sep 10 at 7:47
drhab
89.4k541123
Hints:
$$f_X(x)=int f_X,Y(x,y)dytext and f_Y(y)=int f_X,Y(x,y)dx$$
If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.
answered Sep 10 at 7:47
drhab
89.4k541123
answered Sep 10 at 7:47
drhab
89.4k541123
answered Sep 10 at 7:47
drhab
89.4k541123
answered Sep 10 at 7:47
drhab
89.4k541123
89.4k541123
add a comment |Â
add a comment |Â
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3
You need to consider that $xygeq 0$. The limits will be from 0 to 0.5, or from -0.5 to 0. Either case will result in 1.
– BlackMath
Sep 10 at 7:17