# Not sure if i should post this here

1. Oct 14, 2011

### stonecoldgen

This is from my AP Statistics class and i already gave my super-educated guess, im just posting it here to see how do you guys reason it

Here's the problem:

Suppose you live on scenic Beacon Hill in Boston and decide that, between the high costs of gasoline and parking, owning a car is just not affordable at this time. You're worried, naturally, about how you'll get around but know that you can take advantage of the new and improved public transportation system to get to work and to most of the locations you visit. You will, however, need to take a taxi when shopping for your groceries each week, and being the type of person who worries about everything, you spend many sleepless nights wondering about just how many taxis there are available in Boston.

While on a shopping trip down Boston's historic and fashionable Newbury Street on a beautiful spring day, you notice nine taxis drive by with the following medallion numbers:

594, 1211, 1633, 1195, 108, 697, 825, 474, 286

Assuming that taxi medallion numbers in Boston run in sequence from 1 to N, you'd like to estimate N, the number of taxi medallions ( and hence, the number of taxis ) available in Boston. Thank goodness you're a statistics student!

2. Oct 15, 2011

### M Grandin

According to "Maximum Likelihood" methods the number N of taxis should be chosen so likelihood of actual sample is maximized. Likelihood of any occuring number is 1 / N so if M taxis observed, the likelihood of total sample is (1/N) ^ M which is maximized for minimum possible N, i.e the highest taxi number detected. So N = 1633 should be "expected". That answer may appear counterintuitive - but is what theory suggests, as I understand. But I am neither mathematics professional or student.

3. Oct 15, 2011

### phinds

I assume it's "thank goodness you're a statistics student" because a statistics student is smart enough to know how to pick up the phone and call city hall and ask how many taxis there are.

4. Oct 16, 2011

### HallsofIvy

But what was your "super educated guess"?

5. Oct 16, 2011

### BostonCab

Guys forgive me for joining just to answer you question. There are 1825 legally licensed hackney carriages (taxis) in the city of Boston. Other communities surrounding Boston license their own taxis. Brookline has roughly 100, Cambridge has roughly 300 etc. etc.

There are around 4,400 in the entire Commonwealth of Massachusetts. There are around 9,000 Livery plates in the Commonwealth.

The total number of for hire cars in the Commonwealth is less then the number of Yellow Cabs in Manhattan.

I have a question for you guys though.. how many possible phone numbers are there in an area code.

Take for example area code 617 yxx-xxxx

y can not be the numeral 1 or 0.

6. Oct 16, 2011

### phinds

Well, that leaves all the numbers from 200-0000 to 999-9999 which is 8,000,000

7. Oct 16, 2011

### BostonCab

269 US area codes with 800,000 possible phone numbers each means there are 215 million possible phone numbers. The north American numbering plan will add 1 digit to every phone by 2031 in order to increase the pool of available phone numbers.

How many possible area codes are there ? (yyx)

y can be any digit besides 1 or 0.

8. Oct 16, 2011

### BostonCab

I actually messed that up..

yxx

y can not be 1 or 0

How many potential area codes are there? I am guessing it is a number less than 999? Sorry.. It is hard to write out equations on a steering wheel.

9. Oct 16, 2011

### phinds

all the numbers from 300 to 999, which is 800. This is just the previous question with everything multiplied by 1000