Question

The time between the arrivals of electronic messages at your computer, ?, is exponentially distributed with...

The time between the arrivals of electronic messages at your computer, ?, is exponentially distributed with a mean of two hours.

a) What is the probability that you do not receive a message during a two-hour period?

b) If you have not had a message in the last four hours, what is the probability that you do not

receive a message in the next two hours?

c) What is the expected time between your fifth and sixth messages?

d) Find the three quartiles of the distribution of ?.

e) Determine time ? such that the probability that you wait for a message more than ? minutes

is 0.20. What is the name of ??

Math   Statistics-And-Probability   
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Answer #1

Given that the time between the arrivals of electronic messages at your computer, ?, is exponentially distributed with a mean of two hours. So, the PDF of is

a) The probability that you do not receive a message during a two-hour period is

b) The probability that there was no message in the last four hours is

The conditional probability,

c)The expected time between your fifth and sixth messages is the same as the mean of time between the arrivals of electronic messages at your computer. This nothing but

d) The three quartiles of the distribution of ? is such that

e) We have to find c such that

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