2. (Ex.1 in Section 5.1) A service station has both self-service and full-service islands. On each island, there is a si

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2 Ex 1 In Section 5 1 A Service Station Has Both Self Service And Full Service Islands On Each Island There Is A Si 1 (44.91 KiB) Viewed 31 times

2. (Ex.1 in Section 5.1) A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint PMF of X and Y appears in the accompanying tabulation. P(X = r, Y = y) y=0 y=y=2 I=0 0.10 0.04 0.02 X=1 0.08 0.20 0.06 = 2 0.06 0.14 0.30 (a) What is P(X = 1, Y = 1)? (b) What is P(X <1, Y < 1)? (c) Compute the marginal PMF of X and of Y. Using Pxer). what is P(X < 1)? (d) Are X and Y independent rvs? Explain.