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 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) у 0 1 2 0 0.06 0.09 0.03 1 0.05 a 0.06 2 0.09 0.09 0.18

Please answer all rest questions. Thanks!

Answer 1

LO Page : Date: joint pmf of+4 yus xly O 1 Answers → O 0.06 0:09 0.03 1 0.05 a 2 0.09 0.06 0.18 0.09 0.22 a) a=0.35 b) p(x=1 and Y52) = 0.06 pCX31) = 0.64 d) p (X=1 | =2) = R CRF1 and 432) ply=2) e) EGY KEO) = 0.83 v (71850) = 0.47 3) N 0 pitco, and y=0) # PCX=0). P1430) x and y are not independant h) Ect 2= 1.18 i) ECY) = 1.07 E*4 = 1:37 +) (c(-3) - EC 1) - EC%) F() 1.37 - (1.18 *1.07) : CONCx, y) = 0.107 1) n S.DCA) 0.712 S.D(4) = 0.681 com (x, y) CONCX,Y) JUCI Try) CON (XY) SDC*). SDC4) 0.107 Co. 712)*(0.681) com (4,4) 0.220