Finding Joint Density CDF
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I am working on a problem and am a bit stuck.
It is:
P(X=0, Y=0) = $1over6$
P(X=1, Y=0) = $1over12$
P(X=2, Y=0) = $1over12$
P(X=1, Y=1) = $1over6$
P(X=2, Y=1) = $1over3$
P(X=2, Y=2) = $1over6$
Find the CDF
I understand that we need to plot these points on an x y plane and then draw boundary lines to determine the CDF. I have plotted the points and the form a triangle. What I am confused about, is how do we know where to draw the lines for the boundaries?
probability probability-theory probability-distributions
asked Nov 13 at 17:15
Ethan
9012
add a comment |
up vote
0
down vote
favorite
I am working on a problem and am a bit stuck.
It is:
P(X=0, Y=0) = $1over6$
P(X=1, Y=0) = $1over12$
P(X=2, Y=0) = $1over12$
P(X=1, Y=1) = $1over6$
P(X=2, Y=1) = $1over3$
P(X=2, Y=2) = $1over6$
Find the CDF
I understand that we need to plot these points on an x y plane and then draw boundary lines to determine the CDF. I have plotted the points and the form a triangle. What I am confused about, is how do we know where to draw the lines for the boundaries?
probability probability-theory probability-distributions
asked Nov 13 at 17:15
Ethan
9012
You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am working on a problem and am a bit stuck.
It is:
P(X=0, Y=0) = $1over6$
P(X=1, Y=0) = $1over12$
P(X=2, Y=0) = $1over12$
P(X=1, Y=1) = $1over6$
P(X=2, Y=1) = $1over3$
P(X=2, Y=2) = $1over6$
Find the CDF
I understand that we need to plot these points on an x y plane and then draw boundary lines to determine the CDF. I have plotted the points and the form a triangle. What I am confused about, is how do we know where to draw the lines for the boundaries?
probability probability-theory probability-distributions
asked Nov 13 at 17:15
Ethan
9012
I am working on a problem and am a bit stuck.
It is:
P(X=0, Y=0) = $1over6$
P(X=1, Y=0) = $1over12$
P(X=2, Y=0) = $1over12$
P(X=1, Y=1) = $1over6$
P(X=2, Y=1) = $1over3$
P(X=2, Y=2) = $1over6$
Find the CDF
I understand that we need to plot these points on an x y plane and then draw boundary lines to determine the CDF. I have plotted the points and the form a triangle. What I am confused about, is how do we know where to draw the lines for the boundaries?
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Nov 13 at 17:15
Ethan
9012
asked Nov 13 at 17:15
Ethan
9012
edited Nov 13 at 17:22
asked Nov 13 at 17:15
Ethan
9012
asked Nov 13 at 17:15
Ethan
9012
asked Nov 13 at 17:15
Ethan
9012
9012
You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22
add a comment |
You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22
You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22
add a comment |
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You want to find $P(X leq 0)$, $P(X leq 1)$, etc. and the same for Y. So for example, $P(X leq 0) = frac{1}{6}$
– Jack Moody
Nov 13 at 17:29
Actually you want to find the $P(Xleq x , Yleq y)$ , calculating the Cdf of $X$ and $Y$ will be useful for the estimation of the joint Cdf, iff the random variables are independent.
– Ramiro Scorolli
Nov 13 at 18:06
yes, I understand that but I really don't know how to do that
– Ethan
Nov 13 at 18:08
For example : $F_{X,Y}(0,0)=P(Xleq 0, Y leq 0)=P(X=0, Y=0)=frac{1}6$, $F_{X,Y}(1,0)=P(Xleq 1, Y leq 0)=P(X=0, Y=0)+P(X=1,Y=0)$ and so on
– Ramiro Scorolli
Nov 13 at 18:15
How do we know whether to us x less than or x in between values
– Ethan
Nov 13 at 18:22