Marginal PDF from joint PDF
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$$f_{X,Y}(x,y)~=~begin{cases}2 & if &0< x < 1 ~,~ 0< y< x \[1ex] 0 & text{otherwise} end{cases}$$
Now I should calculate the marginal PDF's.
So I use integral and then I get:
$$f_X(x)~=~int_{0}^{1}2 ~mathrm dy~=2$$
$$f_Y(y)~=~int_{0}^{x}2 ~mathrm dx~=4$$
I just feel like I'm not doing this correct. So if any of you could help me and tell me what I am doing wrong and how to get the correct answer.
statistics density-function
asked yesterday
MiMaKo
588
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up vote
1
down vote
favorite
$$f_{X,Y}(x,y)~=~begin{cases}2 & if &0< x < 1 ~,~ 0< y< x \[1ex] 0 & text{otherwise} end{cases}$$
Now I should calculate the marginal PDF's.
So I use integral and then I get:
$$f_X(x)~=~int_{0}^{1}2 ~mathrm dy~=2$$
$$f_Y(y)~=~int_{0}^{x}2 ~mathrm dx~=4$$
I just feel like I'm not doing this correct. So if any of you could help me and tell me what I am doing wrong and how to get the correct answer.
statistics density-function
asked yesterday
MiMaKo
588
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
$$f_{X,Y}(x,y)~=~begin{cases}2 & if &0< x < 1 ~,~ 0< y< x \[1ex] 0 & text{otherwise} end{cases}$$
Now I should calculate the marginal PDF's.
So I use integral and then I get:
$$f_X(x)~=~int_{0}^{1}2 ~mathrm dy~=2$$
$$f_Y(y)~=~int_{0}^{x}2 ~mathrm dx~=4$$
I just feel like I'm not doing this correct. So if any of you could help me and tell me what I am doing wrong and how to get the correct answer.
statistics density-function
asked yesterday
MiMaKo
588
$$f_{X,Y}(x,y)~=~begin{cases}2 & if &0< x < 1 ~,~ 0< y< x \[1ex] 0 & text{otherwise} end{cases}$$
Now I should calculate the marginal PDF's.
So I use integral and then I get:
$$f_X(x)~=~int_{0}^{1}2 ~mathrm dy~=2$$
$$f_Y(y)~=~int_{0}^{x}2 ~mathrm dx~=4$$
I just feel like I'm not doing this correct. So if any of you could help me and tell me what I am doing wrong and how to get the correct answer.
statistics density-function
statistics density-function
asked yesterday
MiMaKo
588
asked yesterday
MiMaKo
588
asked yesterday
MiMaKo
588
asked yesterday
MiMaKo
588
asked yesterday
MiMaKo
588
588
add a comment |
add a comment |
1 Answer
1
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votes
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1
down vote
accepted
Observe that $$f_{X,Y}=2mathbf1_{(0,1)}(x)mathbf1_{(0,x)}(y)$$
For $xin(0,1)$ we get:
$$f_X(x)=int f_{X,Y}(x,y)dy=int_0^x2dy=2x$$
For $xnotin(0,1)$ the integrand is $0$ so then $f_X(x)=0$.
For $yin(0,1)$ we get:
$$f_Y(y)=int f_{X,Y}(x,y)dx=int_y^12dy=2(1-y)$$
For $ynotin(0,1)$ the integrand is $0$ so then $f_Y(y)=0$.
answered yesterday
drhab
93.5k543125
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Observe that $$f_{X,Y}=2mathbf1_{(0,1)}(x)mathbf1_{(0,x)}(y)$$
For $xin(0,1)$ we get:
$$f_X(x)=int f_{X,Y}(x,y)dy=int_0^x2dy=2x$$
For $xnotin(0,1)$ the integrand is $0$ so then $f_X(x)=0$.
For $yin(0,1)$ we get:
$$f_Y(y)=int f_{X,Y}(x,y)dx=int_y^12dy=2(1-y)$$
For $ynotin(0,1)$ the integrand is $0$ so then $f_Y(y)=0$.
answered yesterday
drhab
93.5k543125
add a comment |
up vote
1
down vote
accepted
Observe that $$f_{X,Y}=2mathbf1_{(0,1)}(x)mathbf1_{(0,x)}(y)$$
For $xin(0,1)$ we get:
$$f_X(x)=int f_{X,Y}(x,y)dy=int_0^x2dy=2x$$
For $xnotin(0,1)$ the integrand is $0$ so then $f_X(x)=0$.
For $yin(0,1)$ we get:
$$f_Y(y)=int f_{X,Y}(x,y)dx=int_y^12dy=2(1-y)$$
For $ynotin(0,1)$ the integrand is $0$ so then $f_Y(y)=0$.
answered yesterday
drhab
93.5k543125
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Observe that $$f_{X,Y}=2mathbf1_{(0,1)}(x)mathbf1_{(0,x)}(y)$$
For $xin(0,1)$ we get:
$$f_X(x)=int f_{X,Y}(x,y)dy=int_0^x2dy=2x$$
For $xnotin(0,1)$ the integrand is $0$ so then $f_X(x)=0$.
For $yin(0,1)$ we get:
$$f_Y(y)=int f_{X,Y}(x,y)dx=int_y^12dy=2(1-y)$$
For $ynotin(0,1)$ the integrand is $0$ so then $f_Y(y)=0$.
answered yesterday
drhab
93.5k543125
Observe that $$f_{X,Y}=2mathbf1_{(0,1)}(x)mathbf1_{(0,x)}(y)$$
For $xin(0,1)$ we get:
$$f_X(x)=int f_{X,Y}(x,y)dy=int_0^x2dy=2x$$
For $xnotin(0,1)$ the integrand is $0$ so then $f_X(x)=0$.
For $yin(0,1)$ we get:
$$f_Y(y)=int f_{X,Y}(x,y)dx=int_y^12dy=2(1-y)$$
For $ynotin(0,1)$ the integrand is $0$ so then $f_Y(y)=0$.
answered yesterday
drhab
93.5k543125
edited yesterday
answered yesterday
drhab
93.5k543125
answered yesterday
drhab
93.5k543125
answered yesterday
drhab
93.5k543125
93.5k543125
add a comment |
add a comment |
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