A service station has both self-service and full-serviceislands. On each island, there is a single regular unleaded pumpwith two hoses. Let X denote the number of hoses beingused on the self-service island at a particular time, and letY denote the number of hoses on the full-service island inuse at that time. The joint pmf of X and Yappears in the accompanying tabulation.

	y
p(x,y)    Â		0	1	2
x	0 Â	  0.10 Â	  0.05 Â	  0.01 Â
1 Â	  0.06 Â	  0.20 Â	  0.08 Â
2 Â	  0.05 Â	  0.14 Â	  0.31 Â

(a) Given that X = 1, determine the conditional pmf ofY—i.e., p_Y|X(0|1),p_Y|X(1|1),p_Y|X(2|1). (Round youranswers to four decimal places.)

y	0	1	2
pY|X(y|1)   Â	   Â	   Â	   Â

(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 thefull-service island? (Round your answers to four decimalplaces.)

y	0	1	2
pY|X(y|2)   Â	   Â	   Â	   Â

(c) Use the result of part (b) to calculate the conditionalprobability P(Y ≤ 1 | X = 2). (Roundyour answer to four decimal places.)
P(Y ≤ 1 | X = 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 theself-service island? (Round your answers to four decimalplaces.)

x	0	1	2
pX|Y(x|2)   Â	   Â	   Â	   Â