Question

Nowadays, movies can be rented from a vending machine located at the entrance to many stores. Suppose that it is now Friday evening at 8pm and a certain machine within a certain store has five copies of the movie "Twilight" available for rent. The machine will not be visited by the owner until Sunday afternoon at noon (which is 40hrs later), at which time returned movies will be restocked. Suppose that customers wanting to rent "Twilight" arrive at this rental machine at a rate of I every 8 hours. Let Wi= the time in hours) until the next "Twilight" renter arrives at the machine. • Name the distribution of W and identify the parameter. Distribution name: Parameter value: • What is the chance the next "Twilight renter arrives sometime on Saturday? Thus, we seek the Pl_< <_) which equals Let X = the number of renters wanting "Twilight that come to the vending machine over the weekend (Fri 8pm until Sunday noon). • Name the distribution of X and identify the parameter. Distribution name: Parameter value: What is the probability that exactly 3 copies of "Twilight" are rented over the weekend? Thus, we seek the P(X= 3) which equals What is the probability that all copies of "Twilight" are rented over the weekend? Thus, we seek P(X___) which equals Hint: Clearly, if exactly five renters show up, they will sell out. Will they sell out if exactly ten renters show up? Yes, the first five will get a copy and the last five won't. How about if exactly twelve renters show up? Twenty? Etc.

Answer 1

time blu Far W: Distribution Name: Exponential distribution, events is. Exponential distribution, Parameters Value; 8 hours - Scale Parameter 1. . B = V (Frate Parameter). on Saturday is from midnight of saturday to 12am Sunday) iwe powsze P (6cW230). . is 1-27*.. CDF ob exponential distribution PCG< W< 30), Þ(W230) - Pllako) = (1-8-'18*30):-(-18x6); P16<W230) - 0.4688

- FJ1X Distribution Name: Die diabilition member of events occuring a fixed interval of time: Parameter value (118)*40 Parameter value = 5 every 40 hours! PDF ob poisson is. Cyke?)/k! (x - 3) = (Sºhaº)15, P(x-3) = 0.007018 For sell out, we need at least 7 oentens to show up, PLX27)= 1-(PLX=0) +PCX=1) +P8X=2)+ P(X= 3) +P[434) ... +P(x=55) +PQ=6)) . 31-65°c)/0!: +(sle-5)/11 + (sfxe5)/2! +(53-5)/3? +(54e5)/4+ (55ES) |s! +(541 (P(x27) 2.1-0.006737 + 0033 6 +0.084 22+ 0.14037+0.1754 + 0.1754). P(x27) = 0.384343]