Question: Consider Example 5 and the probability values given in Figure 1.38. The company has decided that each television set should be given a quality score

Consider Example 5 and the probability values given in Figure 1.38. The company has decided that each television set should be given a quality score calculated in the following manner. A perfect picture scores 4, a good picture scores 2, a satisfactory picture scores 1, and a failed picture scores 0. Also, a perfect appearance scores 3, a good appearance scores 2, a satisfactory appearance scores 1, and a failed appearance scores 0. The final quality score is obtained by multiplying the picture score and the appearance score. For example, the outcome (P, G), where the picture is perfect and the appearance is good, would be assigned a quality score of 4 × 2 = 8.
(a) Construct the probability mass function of the quality score.
(b) Construct the cumulative function of the quality score.
(c) What is the most likely value of the quality score? Recall that an appliance is not shipped if it fails on either the picture or the appearance evaluation, or if it is evaluated as only satisfactory in both cases. How can the probability that an appliance is not shipped be obtained from the cumulative function?

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