Assume there is a dangerous intersection where accidents occur randomly in time
ID: 2921746 • Letter: A
Question
Assume there is a dangerous intersection where accidents occur randomly in time and the number of accidents during an interval of t days is assumed to be Poisson distributed with mean t. The parameter is the daily accident rate. The possible values for are: with respective probabilities 0.1,0.2,0.3,0.2,0.15,0.05) (a) Given that we observe 12 accidents in a six-day period, find the posterior probability distribution for . Y to avoid manual calculations, e.g. R or excel. ou may use a programming language as helpe (b) What is the probability that there will be no accidents during the next week?Explanation / Answer
for 6 day period possible values of ={3,6,9.12.15.24}
therrfore posterior probability P(i|x=12accidents)=pi*e-i*(i)x/x!/(i=16(pi*e-i*(i)x/x!))
from above below is posterior probability distribution of
={
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b)probability of no accidents =(i=09(pi*e-i*(i)x/x!)) =0.05953
0.0001 0.0378 0.3667 0.3842 0.2088 0.0024