A service station has both self-service and full-service islands. On each island

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 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. P(x, y) 0 0.10 0.03 0.01 1 0.06 0.20 0.06 2 0.06 0.14 0.34 (a) Given that X = 1, determine the conditional pmf of Y —.e., Pynx(011), Pnx11, Pyxf211). (Round your answers to four decimal places.) Pyxly1) (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.) Prixy12) (c) Use the result of part (b) to calculate the conditional probability PCY s 11 X = 2). (Round your answer to four decimal places.) P(Y

Explanation / Answer

from above below is joint probability distribution::

a)

dividing each cell in x=1 row with row total below is condition probability distribution:

b)similarly dividing each cell in x=2 row with row total eblow is condition probability distribution:

c)

P(Y<=1|X=2) =0.1111 +0.2593=0.3704

d)

dividing each cell in y=2 column with column total below is condition probability distribution:

x y 0 1 2 Total 0 0.1000 0.0300 0.0100 0.1400 1 0.0600 0.2000 0.0600 0.3200 2 0.0600 0.1400 0.3400 0.5400 Total 0.2200 0.3700 0.4100 1.0000

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