The number of calls (X) that arrive at a hotel reception is modeled as a Poisson

Question

The number of calls (X) that arrive at a hotel reception is modeled as a Poisson distribution with an average of 6 calls per hour (=6 calls/hour= 0.1 calls / min)   

   What is the probability that there are exactly 5 calls in one hour?

   What is the probability that there are exactly 4 calls in 2 hours?

Now, we are interested in the time between calls. Let t (in minutes) be the random variable representing the time between calls.

   What is the distribution (type and parameters) of t and what the mean time is between calls (expected value of t).

   What is the probability that the first call arrives to the reception within 20 min of interval?

   Use the conditional probability rule to calculate the probability that the reception receive a call in the next 30 min, giving that the reception has not had a call in the first 10 min? Compare and comment on the results to question (4).

Explanation / Answer

The number of calls (X) that arrive at a hotel reception is modeled as a Poisson

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