A shipping company records the conditions of cargoes at the delivery points as not damaged (ND), damaged (D), and partially damaged (PD). The following probability mass function was established for three shipping methods:

Determine the marginal probability mass functions PX(x) and PY(y). If a cargo is damaged, what is the probability that it was shipped by sea? By air? By ground? Are the random variables statistically uncorrelated? Why?

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X-Condition of Cargo ND D PD Sea 0.20 0.04 0.02 Y = Shipping Air 0.40 0.02 0.03 Method Ground 0.27 0.01 0.01