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April 23rd, 2017, 11:37 PM   #1
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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)= $1-e^{-x/10}$ 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?
shashank dwivedi is offline  
 
May 23rd, 2017, 01:20 AM   #2
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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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