When you teach at 8am the week after daylight savings time you get to see remnants of the sunrise. Combined with the light snow overnight made for a pleasant bike ride to campus.
You are a contestant on the game show “Lets Make a Deal” and host Monty Hall presents you with a scenario:
Three closed doors, with a shiny new car randomly placed behind only one.
Monty instructs you to pick one door you think has the car behind it. You pick a door, suppose it is the first door, door #1.
Monty: “Now, before we open door #1, lets see what’s behind door #3!”…..no car.
(Monty knows where the car is and would never open that door)
At this point in the game, doors #1 and #2 remain unopened and Monty generously gives you the option of switching from your original choice to door #2.
Since you really want that car, some questions run through your head.
“Should I switch doors or just stay with my original choice? Are my odds of winning even affected by whether I switch or not?”
With two doors unopened doors left, it is intuitive to think that the probability the car is behind either door left is one-half, and therefore it doesn’t matter if you stay or switch doors. Might as well flip a coin to determine which door you end up with.
The preceding thought process is common. Unfortunately, it is also completely wrong and might cost you a car. The truth is you are twice as likely to win if you switch doors.
When Monty revealed a door guaranteed to not have the car, he provided you some valuable information.
To see why this is, start the game over.
1 out of every 3 times you play the game you will pick the winning door to start with. If this happens and you switch doors, you will end up losing.
2 out of every 3 times you will pick a losing door with your initial pick. Here, switching will always end up with you winning the car. This fact is a little more subtle. Monty guarantees you will win if you switch when he revealed what was the only remaining losing door. The only door left to switch to is the one with the car.
In the long run, switching every single time you play will allow you to win twice as often as if you never switched. Simply because you are twice as likely to pick a losing door initially as you are to pick a winning door.
The Monty Hall Problem is an example of the difference conditional probability makes. Given that Monty opens what he knows to be a losing door, a strategy where you always switch is the better one.
For more insight on this problem, check out Wikipedia.
In the last week I have
1) Finished school (M.S. in Statistics from Montana State University)
2) Biked from Bozeman to Missoula (330 miles)
3) Packed my stuff up and moved to Missoula
It has been a big week, and with the Sasquatch Music Festival this weekend the action continues.
Thanks to everyone that helped me get through the last three years. It is crazy to me how fast time passes. Days go by like hours used to when I was little.
The bike trip was epic. I will put up more pictures later. Now I have some unpacking to do.
Last Friday we had the annual Christmas Party. A plethora of goodies always insures a gala event. It was the final hurrah before the cold, stark reality of finals week set in.
Fall goes by quickly in Bozeman. School has been keeping me well occupied these days, but I have managed to take a few pictures of the season on occasion.
I’ve been a little weather obsessed lately. To compliment the snowy pictures here’s what things looked liked around campus last Thursday evening. It was warm, I was in shorts and a sweatshirt. Being from North Carolina it is odd when it stays light until 9 pm but none of the trees have any leaves on them. The grass is getting green though, there is some color emerging from the whites and browns of winter.
It is supposed to be cold for the next couple of days but I know spring can’t be too far away.
I went to Yellowstone over the weekend and took a bunch of pictures but the interweb is being testy so those are going to have to wait.
I’ll be done with my first year of graduate school in about a week. Which is an exciting thought, although it means that I have a lot to do this week. Then about a 10 day break and I’ll teach Stat 216 again for the first summer session, and then almost 2 months of freedom! Hopefully during this time I’ll make it over to see Davy in Tokyo and back to Asheville in August.
It has been warm here for the past week, the grass is bright green and the trees are finally starting to show some color as well.
I hope everyone is doing well and I’ll try to put those pictures up ASAP.
I recently found out that I will I have a job for the first summer school session here teaching Statistics 216. It is the introductory statistics class and what I’m currently teaching. I really enjoy the material and feel like I’m learning a lot to get to the level where I feel comfortable lecturing on it.
It also pays fairly good money (especially for Bozeman). Hopefully it will be all the work I have to do in the summer. I’m also looking forward to having the opportunity to teach this material again so soon, I feel like it will be easier than if I waited a whole summer. Furthermore, the 1st summer sessions ends on June 29th and school doesn’t start again until August 27th! Now I can make definite plans for the summer.
p.s. We have about 7 inches on new snow on the ground as of right now and Bridger is reporting 15 new inches in the last 24 hours. Reminds me I’m living in Montana and it is not quite springtime yet.
School tomorrow. I can handle that I believe. I’m going to start attending a professor’s Stat 216 class so I can see how someone else teaches the material (which can be a little tricky) and learn a few things while I’m at it. Its at 8 am but I’ve been going to bed early enough that its not really a big deal.
Things are going well here. I went to ultimate today for the first time in Bozeman since October or something like that. Since before it got cold and they moved it into a gym, which wasn’t too exciting to me. But I figure ultimate in a gym is better than no ultimate at all. School, snowboarding, and climbing have been running my life since I got back into town.
As I mentioned to Davy I watched this movie “Born into Brothels”. Its a very interesting movie, with a lot of information about India. And it has a very happy ending, which is quite nice. I’m a fan of the happy ending. It also has a lot about photography in it, and it won an Oscar in 2004 for best documentary. Which hopefully An Inconvienent Truth will win this year if people have any sense at all (I’m still debating on this…the people having sense thing).
Life is very good right now. A continuous amount of snowfall between now and April and it will be ridiculous.
Come and visit me in Bozeman. The End
Today is the first day of classes at MSU.Â I have tuesdays and thursdays free so I don’t actually start until tomorrow. I have class at 9, I teach at 11, a class at 1:10, and then I’m done. Not a bad day really, I remember I did the mon, wed, fri schedule in undergrad and it made for some hellish days, but I think this schedule will be quite reasonable.
Its good that I have a free day today because I have a to-do list with approximately a million and one items on it. I’m not going to Bridger today so that I can make a dent in this list. Which will put some pressure on me to actually accomplish things because if I don’t, well, then I should have been at Bridger. (Which got 3″ of new snow yesterday which made for a lovely day).