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In: Statistics and Probability

The occurrence of unplanned shutdown in a manufacturing industry can be considered as a Poisson process....

The occurrence of unplanned shutdown in a manufacturing industry can be considered as a Poisson process. On average, eight shutdown occurs per year.

(a) Calculate the probability that
• the first shutdown occurs during the first quarter;
• more than one shutdown occurs during the first half of the year.

(b) Calculate the conditional probability that the second shutdown will occur during the first half of the year if the first shutdown occurred during the first quarter of the year.

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