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 Plx, y) 0 1 2 0 0.10 0.07 0.05 1 0.04 0.20 0.14 2 0.01 0.07 0.32 (a) What is PCX - 1 and Y - 1)? PX-1 and Y-1) - (b) Compute PCX s 1 and YS 1). PIX S1 and Y S 1) = (c) Give a word description of the event (X+0 and Y0) At most one hose is in use at both Islands One hose is in use on one island. At least one hose is in use at both islands One hose is in use on both islands Compute the probability of this event. PCX and Y 0)

Answer 1

In part d, I left a subpart, P(X less than or equal to 1) = P(X=0) + P(X=1) = 0.15 + 0.34 = 0.49

.P(x1andY) 20 P(x1, YEI): Plo,0)+PO/0)+Pt3,1)+P0, = 0.10+0.074+0.04+0.20 0.41 None of x andY an O x,Y Atleast me house is in use at both islards R() -9) SES eg-P(o) P(o,0)+ Pl 0, 1) +P(o, 2) -O. 10+0.044 0.01 0.05 0.34 0.SL Y 2. O.38 0.40 Pls),22 F(x,0)) 0.10# P(x-0). PY0) Henca Not Iondo perdeut P(XX)R()R4)