conditional and marginal of bivariate t distribution - i.i.d or not?
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I have a bi variate t-distribution with $X=(X_1, X_2)=t(mu, sigma^2, v)$
$$mu=(1,2)',sigma^2=left(begin{array}{cc}
1 & 0\
0 & 1
end{array}right), v=4
$$
How can I calculate the covariance, marginal and conditional distribution $x_2=2$?
Are the distributions i.i.d? If they are, would the marginal distributions and conditional distributions be equal to the univariate distributions?
Am I right in thinking that those two distributions are independent but not identical (because they have a different $mu$? Therefore correlation would be 0?
probability-distributions conditional-probability bivariate-distributions
asked Nov 17 at 15:42
Nickpick
1136
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up vote
0
down vote
favorite
I have a bi variate t-distribution with $X=(X_1, X_2)=t(mu, sigma^2, v)$
$$mu=(1,2)',sigma^2=left(begin{array}{cc}
1 & 0\
0 & 1
end{array}right), v=4
$$
How can I calculate the covariance, marginal and conditional distribution $x_2=2$?
Are the distributions i.i.d? If they are, would the marginal distributions and conditional distributions be equal to the univariate distributions?
Am I right in thinking that those two distributions are independent but not identical (because they have a different $mu$? Therefore correlation would be 0?
probability-distributions conditional-probability bivariate-distributions
asked Nov 17 at 15:42
Nickpick
1136
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a bi variate t-distribution with $X=(X_1, X_2)=t(mu, sigma^2, v)$
$$mu=(1,2)',sigma^2=left(begin{array}{cc}
1 & 0\
0 & 1
end{array}right), v=4
$$
How can I calculate the covariance, marginal and conditional distribution $x_2=2$?
Are the distributions i.i.d? If they are, would the marginal distributions and conditional distributions be equal to the univariate distributions?
Am I right in thinking that those two distributions are independent but not identical (because they have a different $mu$? Therefore correlation would be 0?
probability-distributions conditional-probability bivariate-distributions
asked Nov 17 at 15:42
Nickpick
1136
I have a bi variate t-distribution with $X=(X_1, X_2)=t(mu, sigma^2, v)$
$$mu=(1,2)',sigma^2=left(begin{array}{cc}
1 & 0\
0 & 1
end{array}right), v=4
$$
How can I calculate the covariance, marginal and conditional distribution $x_2=2$?
Are the distributions i.i.d? If they are, would the marginal distributions and conditional distributions be equal to the univariate distributions?
Am I right in thinking that those two distributions are independent but not identical (because they have a different $mu$? Therefore correlation would be 0?
probability-distributions conditional-probability bivariate-distributions
probability-distributions conditional-probability bivariate-distributions
asked Nov 17 at 15:42
Nickpick
1136
asked Nov 17 at 15:42
Nickpick
1136
edited Nov 17 at 18:20
asked Nov 17 at 15:42
Nickpick
1136
asked Nov 17 at 15:42
Nickpick
1136
asked Nov 17 at 15:42
Nickpick
1136
1136
add a comment |
add a comment |
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