So I have a couple of questions regarding marginal, conditional and joint probability mass functions that I need help with. I'll start off with the first question and see if someone can help me with this. I appreciate any help given.

A box contains 4 dice labelled 1,...,4. The die labelled i has i white faces and (6-i) black faces, i=1,...,4. A die is chosen at random from the box and rolled. The random variables X and Y are defined as follows:

X=the number labelling the chosen die

Y={0 if the face showing is black; 1 if the face showing is white

I must construct a table showing the values of the marginal probability mass function for X and a separate table showing the conditional pmf for Y given X=x, for general x.

Now the way I have set the answer out is I have a table with one column $\displaystyle x$ and the other column $\displaystyle P_X(x)$ with x values of 1,...,4 and each $\displaystyle P_X(x)$ as a quarter. Then for the other table I have columns of x=1, x=2,..., x=4 and then the two rows of y=0 and y=1 with $\displaystyle P_{Y|X}(y|x)$ in the top left of the table. Then the values of:

---- x=1 x=2 x=3 x=4

y=0 5/6 2/3 1/2 1/3

y=1 1/6 1/3 1/2 2/3

Sorry if this is hard to understand but is this correct?