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Suppose the number of emails sent from a system follows the Poisson distribution, which averages 30...

Suppose the number of emails sent from a system follows the Poisson distribution, which averages 30 times per hour.
a. Find the probability that an email will not be sent for a certain minute.
b. Let T be a random variable that represents the time between when an email is sent and the next email is sent., Find the probability distribution of T and use this to determine the probability of more than 10 minutes of time between when an email is sent and the next email is sent.

math   Statistics-And-Probability   
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Answer #1

Poisson PMF is

a) The Poisson parameter for 1 minute is .

The probability that an email will not be sent for a certain minute is

b) The time between emails is exponentially distributed with parameter .

The PDF is

The probability of more than 10 minutes of time between when an email is sent and the next email is sent is

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Answer #1

Poisson PMF is

a) The Poisson parameter for 1 minute is .

The probability that an email will not be sent for a certain minute is

b) The time between emails is exponentially distributed with parameter .

The PDF is

The probability of more than 10 minutes of time between when an email is sent and the next email is sent is

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