A car vendor sells type A and type B cars. Consider that X and Y represent the types A and B of cars being sold (respectively). Consider the Random Pair (X, Y) to have probability function according to the table:
| X/Y | 0 | 1 | 2 |
|---|---|---|---|
| 0 | .1 | .075 | .25 |
| 1 | .1583 | .1 | .5 |
| 2 | .075 | .1583 | .1 |
What is the value for the marginal distribution function of Y at the point 1.86?
I'm having trouble understanding this. If I add accumulative values for Y marginal probability I end up with $Y_1 = .33, Y_2 = .43, Y = .33$. First of all, it does not add up to 1. But even then, how do I find the value of the marginal probability at a point that is not in the table? How do I extrapolate the marginal function correctly in order to get its value at 1.86?