EXAMPLE 5.6

In the insurance situation of Example 5.1 and EXAMPLE 5.2 (Example 5.1 continued)

$$p\left(1000,5000\right)=.05\ne \left(.10\right)\left(.25\right)=p_X\left(1000\right)\cdot p_Y\left(5000\right)$$

so $X$ and $Y$ are not independent. In fact, the joint probability table has an entry which is 0, yet the corresponding row and column totals are both positive. Independence of $X$ and $Y$ requires that every entry in the joint probability table be the product of the corresponding row and column marginal probabilities.