GATE 2023 MN – Question 59
Consecutive accident intervals in days are 10, 15, 6, 18, 12, 14, 16, 9, 21, 15, 26, 18, 22, 25, 13. Fit an exponential distribution and find the probability of no accident during a 10-day period, to two decimals.
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Correct answer: 0.52 to 0.56
Explanation
The 15 intervals sum to 240 days, giving mean interval 16 days and fitted rate λ=1/16 per day. The exponential survival function is P(T>t)=exp(−λt). At 10 days this is exp(−10/16)=0.535261, or 0.54. Memorylessness makes the same probability applicable from any observation time under this model.