Question

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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 1 every 8 hours. Let W = 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 PC_<W<_) 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.

please explain and show work for my understanding

Answer 1

PG-Noi-4 Soleition: bien → → dental Machine at rate of levery & hours. Let x = the number of destebution tive copies posameter lalue destrebution Distribution name : Exponential dosterbution time between parametes Value 8hours - Scale Palamele B=1/4 Exponential disturbation is to exx] pG_W230) = P(ne 3o) – p(W26) where - 15 X - 30 Gelle*30) - (i-etietc) - (-0.02351) - (1-0.4703) 0.97649 – 0.5277 0.44899

P410-2 where, k=3 probability 3 Coppies bebore machine (Grey) ki] where, K-3 ... P(x3) = figün 2-15)/3: (ua1.87 * 0.00055)/3! 0.23202 / 6 = 0.03867 Tip(x= 3) = 0.03867 → PCX> = 3) = 1- P(x=0) + p(x-1) + (x=2) + P(X=5) 31-(7.5* e 7-5)/os +(25'46?s)/10 + 7.5? *e75)/a: (2.5**e*7.5)/5!! 1- (0.00055) 40 + (1.5*0.00055)/14,+ (56-25% 0.00055)/a! + (H21-54 * 0-0055), - 0.154G. 0.00418 +0.0151 + I - 0.17412 = 0.8258 .