Question

Ans hould be in detail

Question No 02: [25] A particular area in New Zealand is prone to earthquakes as it is located on the major geological fault line and receives on average 80 earthquakes per day. Keeping in view that the inter arrival time within events of desired interest is independently and exponentially distributed, determine the following: a) What is the average time between two successive earthquakes in that area? b) Given an earthquake has already occurred, what is the probability that the next earthquake occurs within 08hours? c) What is the probability that there is at least al 2hours gap between two earthquakes? d) What is the probability that the particular area in New Zealand is jolted 100 times in a single day?

Answer 1

Let x donote the time between two ealthquake to exponential (resol sollen x=80) dy Ihr a) E(X) = - = -1 1 3 -x24 hrs To = 80 10 324 lo 0.3 hrs b) As, exponentiel distribution has memorgens property, it forgets the previous event. P(x48) - I-e-873 = 0.9999 c.) P(x>12) 1~P(x512) 1- (1-e112) ė -40 ealth quak a de) Let y denote the no. no. of You poisson (n = * [emy ::p (X=100) = e-80 (80)los (1) 0.003939 Note P(x(x) = lor era P(Y=y) = e-> (x)} ll!