From Table 10.1, as completed in Quick exercise 10.2, we see that X and Y are dependent. For instance, P(X = 0, Y = 0) = P(X = 0) P(Y = 0). From Quick exercise 10.2 we know that E[X] = E[Y ] = 1....

From Table 10.1, as completed in Quick exercise 10.2, we see that X and Y are dependent. For instance, P(X = 0, Y = 0) = P(X = 0) P(Y = 0). From Quick exercise 10.2 we know that E[X] = E[Y ] = 1. Because we already computed E[XY ] = 1, it follows that E[XY ] = E[X]E[Y ]. According to the alternative expression for the covariance this means that Cov(X, Y ) = 0, i.e., X and Y are uncorrelated.