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I worked it out in Excel and left it on my home computer. I didn’t save the file but I didn’t close it either. Assuming the other Dr. Pepper doesn’t close it (or any of the other Peppers for that matter) I can repost it this evening.
Dr. P: Any luck?
Calling Dr. P…
Says Who?
Identify the fictional speaker (or thinker) with the quote (some are partial):
3) “Dear me, Mr. Holmes. Dear me!”
icot: are we supposed to know these people or are these comic books we were supposed to have read for homework?
chaverim-
I’m here.
For some reason my posts haven’t been getting through so I’m not going to waste too much time writing a long detailed answer.
As the amount of time on the phone goes to infinity the amount saved by plan A over B or plan B over C approaches 0.
Dr. Pepper: Thanks
I didn’t quite understand your answer. “Amount of time on the phone” calculated “per call” or average monthly usage?
ATTN Mods:
Can you undelete Dr. Pepper’s response from the past few days on this thread?? It was just a mathematical equation… nothing more sinister.
Mod, thx for posting.
Dr. P, I think you are calculating the comparison based on one phone call. The question is of the nature of how much monthly savings a customer with varied usage will save?
i.e. With Plan B (6-second increments) the customers billed savings average 27 seconds per call, compared to Plan C (60-second increments). So the answer can be described in terms of average savings per call.
chaverim-
So for a random number of calls per month, each for a random duration of time?
Do you have a mean and variance for the amount of calls and length or each one or should I set up a random number generator to simulate different possible amounts?
ICOT,
2) Charlie Brown
3) Sherlock Holmes
5) Alfred E. Neuman
7) think it’s from _A Tale of Two Cities_
9) can’t remember the name of Dagwood Bumstead’s (comic strip character) boss
10) Poe’s Raven
Sometimes I play a game with my kids where I mention the name of a pet & they try to guess what book it’s from & what kind of pet it was. It seems that most children’s books have pets & I read aloud a lot to the kids who can’t read yet so nearly everyone can participate in this one.
Dr. Pepper: Yes and yes.
I didn’t necessarily have a mean and variance in mind, but you <i>could</i> use a variance of between 1 second and 30 minutes.
(Also notice Plan B is really 2 plans, the second one being with a 30-second minimum.)
You could describe the savings in terms of time (i.e. seconds per call saved compared to the competing plans) and money (which in effect is the same thing being described monetarily instead of time.)
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?
Dr. Pepper:
Disregard the mean and variance. It is unknown.
There could be any random number of calls per month, and each of them could be any random length.
So the question is only answerable in terms of describing how much the customer will save, on average, on each call. (IOW, it isn’t definable in terms of savings per month.) Sorry for that confusion. (i.e. with 6-second billing [with no minimum per call] vs. 60-second billing, the customer saves an average of 27 billed seconds per call.)
ICOT: as far as #1 goes, I have a feeling you are trying to elicit a response that gives the name of a famous comic book hero’s uncle. But I believe that the actual quote (worded slightly differently) is from W. Churchill. “The price of greatness is responsibility”. Poor old spidey
Dr. Pepper
Member
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.
Dr. Pepper, I know this goes way back, but I did promise to try and stump you one day. I hope I don’t need to work any harder than that to accomplish this.
anon
#3 is dr. watson, not sherlock, elementary.
Says Who? answers
3) “Dear me, Mr. Holmes. Dear me!”, “The Valley of Fear” -Professor James Moriarty
anon for this-
The reading game you described sounds like a fun way to get kids interested in books and reading.
I think that kids who enjoy reading get mental exercise and also pick up useful facts and reasoning skills.
ICOT: Julius Caesar (not really a fictional character – sorry!)
Not at all a fictional characther lol
I hate that poem. The dont write them like they used to (thank god) 🙂
ICOT, another variation on this game is places mentioned in fictional books: for example, Mulberry Street, Klickitat Street, or Privet Drive. My kids are already interested in reading (the ones who can’t read yet like to pretend that they can), but it’s a fun way to talk about what they’ve read.
Just out of curiosity- what is your math background?
Dr. P: I aced the Math regents (~ 95 through 100 on the 3 regents) and college math.
BTW, did the clarification I provided make any more sense to you?
squeak-
Can you pick different parameters? The average length of a phone call is 15 seconds?
Furthermore, if you want to simulate the length of each call, I nead some random numbers (or I can have Excel generate them for me). Could you also find the inverse of F(x) for me (for the Gamma Function)? I never did it before and wouldn’t be surprised if it doesn’t exist in closed form.
I don’t use the hypergeometric distribution on a daily basis so this part might take some extra time (you didn’t stump me though).
chaverim-
I’m still not sure what you’re asking.
Sorry 🙁
I meant 5 as in 5 minutes, so change it to 300 for seconds.
There is no closed form inverse for the gamma (except of course where shape=1). But I didn’t ask for simulation, my question can be answered using means and variances, as you originally wanted.
Dr P,
To put it in a nutshell:
1. How many seconds will a customer save per billed call (on average) if he is billed in 6-second increments, instead of being billed in 60-second increments?
2. How many seconds will a customer save per billed call (on average) if he is billed in 6-second increments with a 30-second per call minimum, instead of being billed in 60-second increments?
3. How many seconds will a customer save per billed call (on average) if he is billed in 1-second increments instead of being billed in 60-second increments?
I’m still not sure why you want to do simulation, and I don’t want to give you any hints, but it seems that if the relevant time period is a month the Central Limit Th. might help you out.
chaverim-
Amount of billable seconds saved (assuming phone calls of random length):
1. 27.0 seconds,
2. Limit as duration goes to infinity is 27.0 seconds
3. 29.5 seconds.
squeak-
You need individual data for this, not grouped data.
Dr. P: Beautiful. Please though clarify what you meant by “Limit as duration goes to infinity”. Duration of any individual call? How do you reconcile that the average billed savings is the same in 1 & 2, considering that calls of 24 seconds or shorter (as some of the random calls are likely to be) have less billable seconds in scenario 1 than 2?
In number one the amount of billable seconds saved for a one second phone call is the same as a 61 second phone call, 121 seconds, 181 seconds…
In number two the amount of billable seconds saved for a one second phone call is different than a 61 second phone call, 121 seconds, 181 seconds… so the average will be different. However the longer the phone call the closer the average will be to 27.0. After 10,000 seconds the average is 27.0032, after 20,000 seconds the average is 27.0018. Keep going towards infinity and the limiting average is 27.0 (although it will never hit 27.0).
Dr P: If you are calculating the savings for a specific phone call, knowing the number of seconds (10,000 and 20,000 seconds in your example), then there isn’t any average savings as you know the precise amount of billable seconds in whatever interval billing you are comparing. Am I not following?
Also, with pure 6-second interval billing the average savings (compared to 60-second) was 27.0 even. Yet in the examples you are demonstrating in your last comment for 6-second with a 30-second minimum, you are calculating average savings of 27.0032 and 27.0018 seconds. Which of course is a greater savings than you calculated for pure 6-second billing. Obviously in no case should 30/6 (scenario 2) have greater savings than 6/6 (scenario 1).
chaverim-
Try looking at all of them as limits. For numbers 1 and 3 the graph of the average will bounce lower and lower hitting bottom at 27.0 and 29.5 respectively, eventually as the number of calls whose duration you take into account approaches infinity the “bouncing” will be so small it will level off at 27.0 and 29.5 respectively.
The graph of the average of number 2 “telescopes” around 27 (think of a backwards telescope that extends forever- it goes higher and lower but the “mountains” and “valleys” get smaller and smaller) as you go along towards infinity. As the number of calls whose duration you take into account approaches infinity the “mountains” and “valleys” will level off at 27.0.
Aah…you math people make my head spin. Can we have some riddles to figure out with plain logic and not functions etc?
This one’s for you squeek.
Someone approached me at college and asked me the following question. On campus I looked like a typical Yeshiva guy and not someone who was taking graduate level courses. (I’m going to translate the secular terms into Hebrew for everyone’s benefit.)
“You people say the 13 Ani Mamins, written by Rambam, every morning. One of them states that Hashem has no body, has no similarities to a body and can not be physically compared to a body at all (# 3 if I remember correctly). I’m currently taking a course called calculus and just learned about infinity. So, if Hashem is infinite then of course he can not have any comparison to a body? Isn’t this extra?”
I figured that he was either trying to harass me or show off that he was taking calculus and wasn’t really interested in the answer. Here’s what I answered;
“Take the graph of y = 1/x and graph it from x = 1 to infinity. Now take that graph and rotate it around the x- axis. The volume is Pi yet the surface area is infinite. This proves that it is possible for an object to have both finite and infinite properties. Therefore Rambam had to include that principal otherwise one might think that Hashem has certain characteristics that are finite and certain characteristics that are infinite.”
When I was done he was standing there in disbelief with his mouth wide open. He had nothing to say so I just walked off.
Very impressive answer!
Might I suggest, though, (since I like to hock) that your example of infinity is a very low order infinity. If I’m not mistaken, the number of points on a two dimensional plane (or even a 3 space shape) is aleph-null. I believe it was Cantor who proved this.
Might not it be impossible for a higher order infinity to have finite properties? Certainly Hashem is the highest order infinte! If so, hadra kusha l’duchta.
A boy was playing baseball and got injured. As he was being rushed to the hospital someone called the ER doctor and said, “you’re son was injured and we’re bringing him to you right away”.
The boy walked into the ER, looked at the doctor and said, “that’s not my father”.
How is it possible that the boy is the doctor’s son but the doctor is not the boy’s father?
The doctor is the boy’s mother.
the doctor was a woman, his mother.
just wondering – which dr. pepper are we talking to here?
Great riddle- which Dr. Pepper am I?
Doctorette.
That was way too easy to have been from the Doctor.
Correct everyone.
Females can be doctors too!
Doc: I think Elizabeth Blackwell was the first to utilize that post-feminist fact?
Until people stop asking me to make them a coffee or to watch their kids while they feed the meter, I think it’s important to publicize that not all women in a doctors office are nurses or receptionist, some are doctors.
So it is okay to ask a nurse to watch the kids or make the coffee, but its beneath a doctor?
I didn’t say it’s OK, I said what happens.
Have you ever seen a male doctor being asked to watch the kids or make a coffee?
Actually I haven’t seen any doctor been asked that.
But I would tend to think a women would be more likely to be asked to watch the kids, as it is more natural for her.
Dr. Pepper,
Are visitors to your office asking you to do these tasks, or are your colleagues doing this? If it’s the former, you may want to consider wearing your white coat.
When my kids were very young, their pediatrician was a woman, and so were many of the specialists they saw. So the first time one of my kids saw a male specialist, I had to explain that doctors could be men too.
anon,
What is so geferlach about being asked to watch children, that you would recommend to go to such lengths (wearing a garment) to specifically avoid such a chesed? (If the person for some reason can’t comply with the request at the time, they can decline. I doubt it is asked so frequently that is truly burdensome.)
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