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April 23rd, 2017, 11:37 PM  #1 
Member Joined: Apr 2017 From: India Posts: 75 Thanks: 0  exponential distribution
Suppose that accidents occur in a large industrial plant at a rate of $\lambda$=1/10 per day. Suppose we begin observing the occurrence of these accidents at the starting of the work on Monday. Let X be the number of days until the first accident occurs. Then the distribution of X is: F(x)= $1e^{x/10}$ for x$\ge$0 = 0 ,x$\lt$0 Now , the source I am referring says that : The probability that the first week is accident free is P[X$\gt$5] = $e^{5/10}$ Well my question is why is it not P[X$\gt$7]?As we are the finding the probability that the first week is accident free that means there should not be accident in the first week and hence my question. Also , the probability that the first accident occurs on Wednesday of the second week is given as: p[7$\lt$X$\le$8] Why is it not calculated between 9 and 10? 
May 23rd, 2017, 01:20 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Can it be assumed that in India, industrial plants do not open on Saturdays and Sundays? If so, then I'm pretty sure the textbook writer had that in mind.


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