# Thread: Marginal Distribution of Rolling 2 Dice

1. ## Marginal Distribution of Rolling 2 Dice

I know this is a simple problem but I can't think the correct way to write it out.

Let X= no. on die 1 and Y= no. on die 2

f(x,y) = {1/13 for x and y = 1,2,3,4,5,6
0 otherwise}

1.Find the marginals of X and Y?

2. Are X and Y independent?
I know they are indepented because f(x,y)=g(x)h(y)
That is true, right?

I just can't come up with the correct way to solve for the marginals. Will each marginal end up just being 1/6?

2. Originally Posted by meks08999
I know this is a simple problem but I can't think the correct way to write it out.

Let X= no. on die 1 and Y= no. on die 2

f(x,y) = {1/13 for x and y = 1,2,3,4,5,6
0 otherwise}

1.Find the marginals of X and Y?
(is that even a probability distribution?)

The marginal distribution of $\displaystyle X$ ( a discrete RV) is defined by:

$\displaystyle \displaystyle Pr(X=k)=\sum_i Pr(X=k,Y=y_i)$

2. Are X and Y independent?
I know they are indepented because f(x,y)=g(x)h(y)
That is true, right?

I just can't come up with the correct way to solve for the marginals. Will each marginal end up just being 1/6?
How can you know this without knowing the marginals?

$\displaystyle f(x,y)=g(x)h(y)$

where $\displaystyle f$ is the joint probability of $\displaystyle X$ and $\displaystyle Y$ , $\displaystyle g$ the marginal for $\displaystyle X$ and $\displaystyle h$ the marginal for $\displaystyle Y$ is a necessary and sufficient condition for independence, but you need to show that it is true (or false).

CB

3. With how you asked if it was a probability distribution, it what I don't understand. I don't see it as a probability distribution either but we were told to find the marginals of this. So, I'm just confused.

I know that I need to prove it true, but I have a strong feeling that it will be true.