Can you help me with E 1. A service station has both self-service and full-service islands.On each island, there is a single regular unleaded pump withtwo hoses. Let X denote the number of hoses being used on theself-service island at a particular time, and let Ydenote the num-ber of hoses on the full-service island in use at that time. Thejoint pmf of Xand Yappears in the accompanying tabulation.yp(x, 3).10.04.02.08.20.06.06.1430a. What is P(X= 1 and Y= 1)?b. Compute P(X<1 and Y< 1).c. Give a word description of the event {X÷0 and Y÷0},and compute the probability of this event.d. Compute the marginal pmf of X and of Y. Using (x),what is P(X< 1)?e. Are Xand Yindependent rv's? Explain.2. When an automobile is stopped by a roving safety patrol,each tire is checked for tire wear, and each headlight ischecked to see whether it is properly aimed. Let X denote thenumber of headlights that need adjustment, and let Y denotethe number of defective tires.a. If X and Y are independent with p(0) = .5, p(1) = .3,P;{2) = .2, and p;(0) = 6, p;(1) = .1. p;(2) = P{3) = .05,and p;(4) = .2, display the joint pmf of (X, Y) in a jointprobability table.%3D

Name: Can you help me with E 1. A service station has both self-service and
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Can you help me with E 1. A service station has both self-service and full-service islands.On each island, there is a single regular unleaded pump withtwo hoses. Let X denote the number of hoses being used on theself-service island at a particular ti