## A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. L

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 0.01

1 0.08 0.20 0.06

2 0.05 0.14 0.33

(a) Given that X = 1, determine the conditional pmf of Yi.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)

## Answers ( )

Answer:(a)(b)Step-by-step explanation:GivenSolving (a): Find PMF of y if x = 1This implies that, we consider the dataset of the row where x = 1 i.e.

The PMF of y given x is calculated using:When x = 1— the sum of the rowsSo, we have:For i = 0 to 2, we have:So, the PMF of y given that x = 1 is:Solving (b): The interpretation of (b) is to find the PMF of y if x = 2This implies that, we consider the dataset of the row where x = 2 i.e.

WhenSo, we have:For i = 0 to 2, we have:So, the PMF of y given that x = 1 is: