2. An art collector travels to art auctions once a month on the average. Each trip is...

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2. An art collector travels to art auctions once a month on the average. Each trip is guaranteed to produce one purchase. The time between trips is exponentially distributed. Determine the following:

(a) The probability that no purchase is made in a 3-month period.

(b) The probability that no more than 8 purchases are made per year.

(c) The probability that the time between successive trips will exceed 1 month.

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