Trying to do this question.
Finding K i get 1/25 but I know this is wrong.
MY method P(1,1) + P(1,3) + P(2,3) = 1
Thanks in advance for your help.
Cool Thanks so much! Im glad i was on the right track.
Does that same idea hold for when Im getting the marginal function of X
I get 2x^2 / 25 + 10/25 which is getting X over all values of Y where Y can be 1 or 3.
But is it also possible say for x = 1 and y = 50 for example which would still give a value for X even though the joint would give 0?
Perhaps it'll be clearer if you see it written this way :
Let $\displaystyle \mathcal{X}$ be the domain of X, namely {1,2}
Let $\displaystyle \mathcal{Y}$ be the domain of Y, namely {1,3}
Then for any $\displaystyle x\in\mathbb{R}$, we have :
$\displaystyle f_X(x)=P(X=x)=\sum_{y\in\mathcal{Y}} P(x,y)=P(x,1)+P(x,3)$
Which exactly gives what you got :
if x is in $\displaystyle \mathcal{X}$2x^2 / 25 + 10/25
If $\displaystyle x\neq 1,2$, we still have $\displaystyle f_X(x)=P(x,1)+P(x,3)$, but then these values are 0, according to the definition of P(.,.)