Conditional probabilities involving functions of random variables and the variables
I have that $Z = X + 2Y$. $X, Y$ are independent. I know $f_X(x), f_Y(y), f_{X,Y}(x,y)$ and $f_Z(z). $ How can I find $f(x,y|z)$?
I know that $f(x,y|z) = f(x, y, z)/f(z) = f(z| x, y)*f(x, y)/f(t)$ but i'm stuck because I can't find $f(x, y, z)$ or $f(z| x, y)$. Which strategies can I use?
I would also appreciate if someone can recommend me a book or a page with results involving conditional probability and sums/functions of random variables, independent or not.
Thanks in advance.
conditional-probability
asked Dec 26 at 10:55
Bruce Kane
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I have that $Z = X + 2Y$. $X, Y$ are independent. I know $f_X(x), f_Y(y), f_{X,Y}(x,y)$ and $f_Z(z). $ How can I find $f(x,y|z)$?
I know that $f(x,y|z) = f(x, y, z)/f(z) = f(z| x, y)*f(x, y)/f(t)$ but i'm stuck because I can't find $f(x, y, z)$ or $f(z| x, y)$. Which strategies can I use?
I would also appreciate if someone can recommend me a book or a page with results involving conditional probability and sums/functions of random variables, independent or not.
Thanks in advance.
conditional-probability
asked Dec 26 at 10:55
Bruce Kane
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I have that $Z = X + 2Y$. $X, Y$ are independent. I know $f_X(x), f_Y(y), f_{X,Y}(x,y)$ and $f_Z(z). $ How can I find $f(x,y|z)$?
I know that $f(x,y|z) = f(x, y, z)/f(z) = f(z| x, y)*f(x, y)/f(t)$ but i'm stuck because I can't find $f(x, y, z)$ or $f(z| x, y)$. Which strategies can I use?
I would also appreciate if someone can recommend me a book or a page with results involving conditional probability and sums/functions of random variables, independent or not.
Thanks in advance.
conditional-probability
asked Dec 26 at 10:55
Bruce Kane
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have that $Z = X + 2Y$. $X, Y$ are independent. I know $f_X(x), f_Y(y), f_{X,Y}(x,y)$ and $f_Z(z). $ How can I find $f(x,y|z)$?
I know that $f(x,y|z) = f(x, y, z)/f(z) = f(z| x, y)*f(x, y)/f(t)$ but i'm stuck because I can't find $f(x, y, z)$ or $f(z| x, y)$. Which strategies can I use?
I would also appreciate if someone can recommend me a book or a page with results involving conditional probability and sums/functions of random variables, independent or not.
Thanks in advance.
conditional-probability
conditional-probability
asked Dec 26 at 10:55
Bruce Kane
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 10:55
Bruce Kane
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 10:55
Bruce Kane
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 10:55
Bruce Kane
61
asked Dec 26 at 10:55
Bruce Kane
61
61
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Bruce Kane is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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