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 Y denote the number of hoses on the full-service island in use at that time. The joint probability mass function of X and Y appears below:
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
Given that X = 1, determine the conditional pmf of Y i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1).