Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|1) (b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.) y 0 1 2 pY|X(y|2) (d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.)
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 | 0.03 | 0.02 |
| 1 | 0.07 | 0.20 | 0.08 | |
| 2 | 0.05 | 0.14 | 0.31 |
| y | 0 | 1 | 2 |
| pY|X(y|1) |
(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.)
| y | 0 | 1 | 2 |
| pY|X(y|2) |
(d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.)
| x | 0 | 1 | 2 |
| pX|Y(x|2) |
Let X = the no. of hoses being used on the self-service island at a particular time.
Y = the no. of hoses on the full-service island in use at that time.
The joint pmf of (X, Y) is,
| y | |||
| x | 0 | 1 | 2 |
| 0 | 0.1 | 0.03 | 0.02 |
| 1 | 0.07 | 0.2 | 0.08 |
| 2 | 0.05 | 0.14 | 0.31 |
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