Entries Tagged 'Probability' ↓

This is a pretty cool article that talks about how weather forcasters try to predict were a hurricane will go and how hard it will hit. It talks about why the graphs you see on TV look the way they do (they are based on the probability models the computer generates based on current conditions and past storms). Good to know information so that you can “read” the maps they show on TV.

I keep hearing all these stories about people making mega-bucks with adsense on their blogs. The idea of making money on the internet is interesting to me (after all I have ads on this page) but it seems strange to me that people could be making 6 figures just by blogging.

What’s even more puzzling is the high priced keywords that apparently a lot of people make money off of. Googling for phrases like “top keyword” will get you all kinds of sites that tell you words like “casino”, “gambling”, “debt”, “mortgage”, “loan”, anything or anyone having to do with sex or porn, and really odd ones like “Donate Car” and “Answering Service”. Basically anything that would appear in your normal spam message. (With the exception of “Rolex” I get a lot of spam about watches, yet I saw nothing to indicate its a new keyword…)

I guess that sites that focus on these keywords get a good ranking on Google and therefore get a lot of traffic which in turn brings in a lot of money. But it seems weird to me, like if Google wanted to they could probably stop this.

I think the reason some people are getting so rich with so little content is because the system isn’t in equilibrium: The results of the search are skewed in favor of the keyword laden blogs. Since Google is all about delivering good results, it would seem they would want to focus on “legitimate” sites (i.e. give the search a link to a casino instead of a link to a page advertising casinos), and that would balance the system by sending the traffic to useful sites.

It would seem that simply monitoring spam traffic (to see what topics are most popular) would be a good way to see which way the scales are tipping. Then they could adjust their ranking system to ensure that sites that would be a probable target for those keywords would rise to the top, as opposed to the sites that are playing the odds by making themselves statistically more appealing (i.e. keyword stuffing, etc.).

But then again there’s a reason why those keywords are the “top keywords”, its because someone out there is willing to pay that much to get the traffic of people interested in that topic. So maybe the system is ok, and I’m just looking at it funny. That could be the reason why I’m a better coder than a business man…

From Slashdot I found this article:How Much Does iTunes Like My Five-Star Songs? In it the author tackles the subject of iTunes and how t picks songs. Its an interesting read and it pretty much confirmed a lot of what I thought about how iTunes works.

Although I do disagree with the assertion about the hypothetical playlist, the author claims that most songs in a persons collection will be rated at 3 stars, and the distribution of rankings will follow a bell curve. In my collection that is most definitely not the case. The majority of my songs are in the 4 and 5 star range, with a smattering of 3 stars, very few 2 stars, and growing number of 1 stars.

For me, I want to hear songs I like (4 and 5 star) more often, so when I hear an unrated song I like I’m more likely to rate that songs. For songs that are ok, I’ll eventually rate them 3 stars. Songs I really don’t care for get the 1 star. Since I imported all of my mp3’s with no rankings I’ve got a mountain of unrated songs. Perhaps this is the wildcard: once I get the majority of my songs rated perhaps they will fall into a bell curve, but I am doubtful of this because of my tendency to get rid of songs/albums/artists I don’t like. i.e. If I can’t rate a single song on an album over 1 or 2 stars, then why bother keeping it?

But that’s just me.

The MAA website is constant source of interesting bits of information. Today while reading Ivar’s new column I saw a link to an older article called Random Home Runs where he discusses the topic of "Do baseball hitters have streaks?". I highly recommend the article, its very enlightening.

Tags: Statistics

Today while looking at the Mathematical Association of America website (they have really great columns there every month) I saw this article article by Keith Devlin where he talks about some statistics that were reported in a newspaper. His point is that if they are read wrong, statistics can be used to mislead people in a big way. I really wish more people would read articles like this, that way when confronted with newspaper articles reporting a 95% increase in <insert bad thing here> they will be able to look objectively at the numbers and decide if what is being reported is probable or if it is meant to scare.

A lot of people don’t realize that just because something is possible, it does not mean it is probable.

Tags: probability, possibility, stats

 I was thinking about the coin flipping topic again. I decided to code up a quick little python program to simulate X number of coin tosses. I ran it for several numbers of X (I think the largest was 100000) and it seems to be that most of the time it came out close to 50-50.

 Now a quick disclaimer: I have no idea how random the randrange function is, so this program should be taken with a gain of salt.

 How it works: You give it a number which is the number of coin tosses you want it to do. Say 100 for example. Then it takes this number and proceeds to call random.randrange() with a minimum number of 1 and a max of 100 million. (note this is an odd number and an even number). It then takes the result (somewhere inclusive to that range) and does a modulus 2 operation on it to see if it is even. If it is, it increments the heads counter if it isn’t the tails counter gets incremented.

 At the end of the tosses it then reports back the numbers for heads and tails. Its a decent simulation I think, and somewhat representative of what you would see if you did this in real life. A more accurate simulation would probably take into account which side of the coin was facing up when it was first flipped (see my previous posting for details on that), and it would also probably make sure the random number generator was properly seeded before every toss…. But like I said, this is a quick little demo program. Feel free to modify it.

coinflip.py (Please note you need to save it with a .py extension, I had to put the .txt on there to get it to load onto geocities.)

After a converation at work about the flipping of a coin (and is it really a 50-50 chance of heads or tails), I came across this article today. Its seems that there some catches to the statement I made yesterday.

Research has found that there does seem to be a bias when flipping a coin, it seem that a coin is more likely to land on the same face it started out on. So if its heads up when you flip it, it is more likely that it will be heads up when it lands. I’ll be sure to remember that next time someone asks if I want to flip for something…

This weekend I finished reading the memoirs of Dr. Edward Teller (he helped invent the atomic and hydrogen bombs). In his later years Dr. Teller was involved with a lot of foundations to try and help get people into the field of “Applied Science” (think hands-on practical science instead of pure theory)

He recounted an interesting story (pg. 487) about one of the interview questions he used to ask applicants: If you flipped a coin and each time bet a penny on the outcome of the flip (i.e. 1 penny it would land on heads, etc.), how much money would you have at the end of 1,000 tosses?

He said a lot of people had trouble with this one. The answer is close to 0. Why? Each toss of the coin has a 50% chance on landing on heads (or tails). If you toss the coin enough times, you will start to see that you have tossed almost an equal amount of heads and tails. Betting a penny on each toss means that you would come out almost even in the end.

Why almost even? Each coin toss has nothing to do with any past or future toss. It is possible to toss 100 tails in a row, but this is
unlikely. (i.e. it has a low probability) 10 in a row is possible, as is 3, and each of those is more likely than the previous one. So when you
get to the 998th toss, if you have tossed exactly 500 heads and 498 tails, it is possible you could flip 2 more heads in a row giving you a net profit of 2 cents (assuming you bet on heads). Neat huh?