service station has both ser service and full service islands on each island the

Question

service station has both ser service and full service islands on each island there is a single regular unleaded pump with two hoses. Let X denote the number or noses being used on the ser service i land a a particular t me, and let Y denote the number ot the full-service island in use at that time. I he joint pmf of x and appears in the accompanying tabulation. ses n 0.10 0.3 0.02 0.0 0.20 0.06 20.00 0.1 0.3 (a Given that X 1, detertnine the conditi nel pmf on ' e Pr x 1 Pr x(1/1), pylr 211). Round your answers to four decimal places. b) Given that two huses are in use at the self-sevice islarid, what is the coriditional pmf uthe number uf hoses in use on the full-service island (Rourid your answers to four decimal places.) Ic) Use the result of part (b) to calculate the concitional probabiity tY1X-2). (Round your answer to tour decimal plaoes. (d) Glwn that two hnse, ar in lite at me fuli-servica Island, what ls thea conditional pmf af the numher in lit , at the self-ser Ica island? (Round yournswer, to four caclmal places.

Explanation / Answer

from above joint probability:

a) dividing each cell in x=1 row ; by row total below is Y|X

b)

similarly:

c)P(Y<=1|X=2) =0.1132+0.2642 =0.3774

d)

y x y1 y2 y3 Total x1 0.1000 0.0300 0.0200 0.1500 x2 0.0600 0.2000 0.0600 0.3200 x3 0.0600 0.1400 0.3300 0.5300 Total 0.2200 0.3700 0.4100 1.0000

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