Question

3. At the Direct cable system claim center, the reported service request usually follows Poisson distribution with rate of 5 /day (Assume 1 day is 24 hours unit). (a) Find the probability that there will be fewer than 3 requests on a given day [5] (b) Find the probability that the time until the next request is less than two hours. [Hint: The inter-arrival time of request is distributed as Exponential distribution] 157

Answer 1

Answer Given data- sovice request follow possion distribution. rate of occuessence of sunrice bequest 51 dag = Tet x be the sandom variable which is request on a given day (say) for mellae used P(x= x) = ex of occurence d=ast, whese x % average no of swice request (9) x = 5/ day & 1 day (given ) P (x=x) of tawes than 8 request means x=0, x= 1, no 2 P(x<8) - P(x=0) + P(x-1) + P (X=2) P (x<s) 0.1246 anvel now are to the question the inter arrival request follows exponential distrubtion therefore it's Probabrity density function will be f(x) = 3 e-xx (say has exponential dissibution & is rate of accusance which / 24 hours n (say) random variable shows inter-assival request

fas P(x<2) = 1- e-da P(X> x = ein acc to the question P ( x 2) = 1- (- 24 h 1-6-512 P(x<27= 0.3407