First, the map (bigger version here). This map shows where the jobs posted during last weekend's job postings are located. A slightly more interactive version is available here, but takes forever to load.

Yes, there is a job WAY up in the Arctic, and 28 people applied to it. I could have sworn too that there used to be jobs in New Zealand, Hawaii and Australia, but oh well.

A similar map counting the number of applications going to each city is available here (this also takes forever to load). However the two maps look pretty much the same, since the resolution of the bubbles are not that great.

What's also not clear in the maps is the actual number of jobs in Waterloo and Toronto areas. To make it clear, here are the top 10 locations with the most number of job openings.

If we take the top 10 locations with the most number of applications, we get something similar.

Now what happens when we look at the cities that get the most applications per opening? We get something COMPLETELY different.

The more "exotic" places like Saint-Hubert (where the Candian Space Agency is located), California and others don't offer many jobs, but the ones that are offered attract a lot of applications. Note though that I would take the exact ordering in the last chart with a grain of salt for two reasons: (1) the position that actually attracted the most number of applications is offered in "Various Locations" -- take a WILD guess what company offered that position (hint: start's with a "G") and (2) a lot of companies lie about the number of openings they have.

What about the places with the lowest applications per job?

I'll leave you to come up with your own conclusions here.

Finally, a note about data and methodology. Jobmine is the system co-op students/employers at Waterloo use to manage job postings and applications. Job name, location, opening and applications data were pulled off of Jobmine 8am this morning (posting closed 12am last night). Some location names are changed slightly to avoid multiple entries per name, and so that Google's Geomap tool would map it correctly (it mapped "London" to "London, England", etc.). When a job opening was in multiple locations, I took the first one. Jobs that put "Multiple Locations" or "Various" or something ambiguous as their location were deleted.

I plan to squeeze more goodies out of this data, so stay tuned. Incidentally, if you are familiar with Google Charts API and know how to make it go faster, please let me know.

End of Entry

## Wednesday, May 19, 2010

## Wednesday, May 5, 2010

### Monty Hall Problem: an intuitive explanation

The Monty Hall Problem is a probability puzzle based on a TV show. Here's the puzzle:

Here's the answer: you should switch. I'll give two explanations as to why. The first one will (hopefully) appeal to your intuition, and the second one will be an argument using probability.

The Intuitive Explanation

Let's change the game for a bit. Suppose instead of only 3 doors, we have 100 doors: with 99 goats still only one car behind the doors. After you pick a door (say door A), the host opens 98 doors to reveal 98 goats, only leaving one other door (say door B) closed. In this case, would you choose to switch (to door B)? Again think about this first before reading on.

The Probabilistic Explanation

Here's how you might have reasoned about the previous scenario: the only case where switching to door B is not beneficial is when you choose the right door the first time. That only has a 1% chance of happening.

The same reasoning applies to the 3 doors scenario. The only case where switching would not help you is when you choose the door with the car behind it the first time. There's a 33% chance of that happening, and a 66% chance of picking the wrong door. Thus you will double your probability of winning the car if you decide to switch.

End of Entry

Suppose that you are on a game show, and the host shows you three doors. He tells you that behind two of the doors are goats, and behind one of the doors is a brand new luxury car. He asks you to pick one of the three doors, and if you picked the door with the car behind it, you keep the car. You pick a door (say door #1). The host, knowing which door has the car behind it, walks over to a different door (say door #2) and opens it to reveal a goat. He then offers you to a chance to change your mind (and switch to door #3). Should you make the switch?If you haven't heard the puzzle a billion times already, think for a bit before reading on.

Here's the answer: you should switch. I'll give two explanations as to why. The first one will (hopefully) appeal to your intuition, and the second one will be an argument using probability.

The Intuitive Explanation

Let's change the game for a bit. Suppose instead of only 3 doors, we have 100 doors: with 99 goats still only one car behind the doors. After you pick a door (say door A), the host opens 98 doors to reveal 98 goats, only leaving one other door (say door B) closed. In this case, would you choose to switch (to door B)? Again think about this first before reading on.

The Probabilistic Explanation

Here's how you might have reasoned about the previous scenario: the only case where switching to door B is not beneficial is when you choose the right door the first time. That only has a 1% chance of happening.

The same reasoning applies to the 3 doors scenario. The only case where switching would not help you is when you choose the door with the car behind it the first time. There's a 33% chance of that happening, and a 66% chance of picking the wrong door. Thus you will double your probability of winning the car if you decide to switch.

End of Entry

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