3.+10 points My Notes Ask Your A service station has both self-service and full-

Question

3.+10 points My Notes Ask Your 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 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 appears in the accompanying tabulation. p(x, y) 0 0.10 0.03 0.02 10.07 0.20 0.07 2 0.06 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y-i.e., pnx(011), pylx(111), x(211). (Round your answers to four decimal places.) Pyxyl1) (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.) Pyix(y12) (c) Use the result of part (b) to calculate the conditional probability P(Y 1 X-2). (Round your answer to four decimal places) (d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.) Pxlx12) Read It Talk to a Tutor Submit Answer Save Progress Practice Another Version

Explanation / Answer

from above joint distribution table is as follows:

a)dividing each cell in x=1 row ; with row total below is conditional pmf of y:

b) similarly:

c)

P(y<=1|X=2)=0.1176+0.2745 =0.3922

d)

similarly as above for y=2 column divide each cell with column total:

please revert for any clarification.

y x 0 1 2 Total 0 0.1000 0.0300 0.0200 0.1500 1 0.0700 0.2000 0.0700 0.3400 2 0.0600 0.1400 0.3100 0.5100 Total 0.2300 0.3700 0.4000 1.0000

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