A service station has both self-service and full-service islands. On each island, there is a single regular
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Question:
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.
y | ||||
p(x, y) | 0 | 1 | 2 | |
x | 0 | 0.10 | 0.05 | 0.02 |
1 | 0.06 | 0.20 | 0.07 | |
2 | 0.05 | 0.14 | 0.31 |
(a) What is P(X = 1 and Y = 1)?
(b) Compute P(X 1 and Y 1).
(c) Compute the probability of this event.
(d) Compute the marginal pmf of X.
x | 0 | 1 | 2 |
---|---|---|---|
pX(x) |
Compute the marginal pmf of Y.
y | 0 | 1 | 2 |
---|---|---|---|
pY(y) |
(e) Using pX(x), what is P(X 1)?
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