Reply To: The Riddle Thread….

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squeak
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Dr. Pepper

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chaverim-

I’m not sure I’m following you.

There are many different possible values for a “variance of between 1 second and 30 minutes”. (There are also many different possibilities for the mean between 1 second and 30 minutes.)

I would also need parameters for the number of calls. (Feel free to throw in a discrete distribution if you feel it will be a better fit for the data.)

Just out of curiosity- what is your math background?

I think the more relevant question may be, what is his telecom background? 🙂

Dr. P, use a Poisson with a mean of 8 for calls per day, and a gamma with shape parameter = 3 and scale parameter = 5 for duration. If that is too easy, you can also answer part B. Use a binomial with p = .75 for calls answered hypergeometric to determine whether or not the unanswered calls leave voicemail.

Part C. Those that leave a voicemail need to be called back, so include the call-back in your analysis, using the assumptions given in part A.

Part D. If you call back, there is still only a 75% probability that the return call will be answered, but a 100% probability that you will leave a voice message. Factor in the cost of returning calls and leaving voice messages.

Part E. Determine the odds of playing phone tag indefinitely.

Part F. Determine the profit margin for each company, assuming that their internal cost is 1 cent per connection plus 60% of the duration cost that they pass on to you.