## 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

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 0.03 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)

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2 days 2021-07-22T01:22:41+00:00 1 Answers 0 views 0

## Answers ( )

(a)

(b)

Step-by-step explanation:

Given

Solving (a): Find PMF of y if x = 1

This 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 rows

So, 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 = 2

This implies that, we consider the dataset of the row where x = 2 i.e.

When

So, we have:

For i = 0 to 2, we have:

So, the PMF of y given that x = 1 is: