Joint Discrete Random Variables
We roll two dice, and define the random variables X and Y as below.
X : The absolute difference between the rolls.
Y : The minimum of the rolls.
(a) (5 Pts.) Determine the outcomes, and then the values of the random variables.
(b) (5 Pts.) Determine $p_{XY}[x, y]$, and then from $p_{XY}[x, y]$ determine, $p_X[x]$ and $p_Y [y]$.
(c) (5 Pts.) Determine $Cov(X, Y)$ and $rho_{XY}$.
(d) (5 Pts.) Determine the joint CDF. Then, from the joint CDF obtain marginal CDFs.
Show the CDF values in a table with axis x and y.
probability
edited 2 days ago
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asked 2 days ago
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add a comment |
We roll two dice, and define the random variables X and Y as below.
X : The absolute difference between the rolls.
Y : The minimum of the rolls.
(a) (5 Pts.) Determine the outcomes, and then the values of the random variables.
(b) (5 Pts.) Determine $p_{XY}[x, y]$, and then from $p_{XY}[x, y]$ determine, $p_X[x]$ and $p_Y [y]$.
(c) (5 Pts.) Determine $Cov(X, Y)$ and $rho_{XY}$.
(d) (5 Pts.) Determine the joint CDF. Then, from the joint CDF obtain marginal CDFs.
Show the CDF values in a table with axis x and y.
probability
edited 2 days ago
gt6989b
33.1k22452
asked 2 days ago
Kelly
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
1
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago
add a comment |
We roll two dice, and define the random variables X and Y as below.
X : The absolute difference between the rolls.
Y : The minimum of the rolls.
(a) (5 Pts.) Determine the outcomes, and then the values of the random variables.
(b) (5 Pts.) Determine $p_{XY}[x, y]$, and then from $p_{XY}[x, y]$ determine, $p_X[x]$ and $p_Y [y]$.
(c) (5 Pts.) Determine $Cov(X, Y)$ and $rho_{XY}$.
(d) (5 Pts.) Determine the joint CDF. Then, from the joint CDF obtain marginal CDFs.
Show the CDF values in a table with axis x and y.
probability
edited 2 days ago
gt6989b
33.1k22452
asked 2 days ago
Kelly
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
We roll two dice, and define the random variables X and Y as below.
X : The absolute difference between the rolls.
Y : The minimum of the rolls.
(a) (5 Pts.) Determine the outcomes, and then the values of the random variables.
(b) (5 Pts.) Determine $p_{XY}[x, y]$, and then from $p_{XY}[x, y]$ determine, $p_X[x]$ and $p_Y [y]$.
(c) (5 Pts.) Determine $Cov(X, Y)$ and $rho_{XY}$.
(d) (5 Pts.) Determine the joint CDF. Then, from the joint CDF obtain marginal CDFs.
Show the CDF values in a table with axis x and y.
probability
probability
edited 2 days ago
gt6989b
33.1k22452
asked 2 days ago
Kelly
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
gt6989b
33.1k22452
asked 2 days ago
Kelly
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
gt6989b
33.1k22452
edited 2 days ago
gt6989b
33.1k22452
edited 2 days ago
gt6989b
33.1k22452
33.1k22452
asked 2 days ago
Kelly
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Kelly
6
asked 2 days ago
Kelly
6
6
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Kelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
1
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago
add a comment |
2
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
1
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago
2
2
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
1
1
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago
add a comment |
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2
Welcome to MSE. Please provide your thoughts on how you are solving it and where you got stuck so we can help.
– Will M.
2 days ago
I'm sorry, but I have no idea. I'm bad at probability.
– Kelly
2 days ago
1
@Kelly you must have some idea. Review your notes, check your textbook for similar examples worked through. One does not learn by sitting idly.
– LoveTooNap29
2 days ago