Question

explain as much as possible, thanks

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 y 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 y 1 0.03 0.20 0.14 0.10 0.06 0.06 2 0.02 0.07 0.32 1 2 (a) Given that X = 1, determine the conditional pmf of Y-i.e., Prix(011), Prix(1/1), Prix(2/1). (Round your answers to four decimal places.) 0 у Prix(y11) (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.) у 2 Prix(12) 0 1 (c) Use the result of part (b) to calculate the conditional probability PCY<1 X = 2). (Round your answer to four decimal places.) PCY <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 the self-service island? (Round your answers to four decimal places.) X 0 2 Pxy(x2)

Answer 1

	y
x	0	1	2	total
0	0.1	0.03	0.02	0.15
1	0.06	0.2	0.07	0.33
2	0.06	0.14	0.32	0.52
total	0.22	0.37	0.41	1

a)

for p(y|1) =P(y,1)/P(x=1) =P(y,1)/0.33

y	0	1	2
p(y|1)	0.1818	0.6061	0.2121

b)

y	0	1	2
p(y|2)	0.1154	0.2692	0.6154

c)

P(y<=1|2)=0.1154+0.2692 =

0.3846

d)

x	0	1	2
P(x|2)	0.0488	0.1707	0.7805