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27 would be correct if each side were independent random variables rather than the cube of a random variable. The way the problem is set up you are suppose to solve for E[a^3] (the third moment of the random variable) rather than (E[a])^3.

It is important to note the sample set of the survey: "The researchers surveyed 655 students entering Berea College, a private liberal arts college located in Kentucky, in the falls of 2000 and 2001."

I have a feeling that the results of the survey would be different at a public university with strong science and engineering programs.

My personal experience has been that many people will change their intended degrees, but rarely have I seen someone completely withdraw from science or engineering programs

It was really only a matter of time before this happened, regulation of trade (and the taxation thereof) is one of the main tasks of a government.

Awesome idea to help make capturing data more easy, but how will you deal with the problem of the curse of dimensionality? As you start to capture more variables you data begins to appear far apart leading to less meaningful results.

Also, while 'capturing everything' sounds like an awesome idea it can lead to worse performance if you don't take into account that your data now has more variables that can each introduce noise.

The author's argument for this post is rather poor. He states that the raw data plot is noisy and weakly correlated, thus no relationship can be drawn by averaging the data into sets of buckets.

While the author is correct in that averaging hides the variance of data, he does not try to answer the question of "Can a trend be found from noisy data?" or show other accepted statistical methods that show no correlation in the data.

Instead the author dismisses the report from Gates through name calling: "It seems like the point of this ‘research’ is to simply ‘prove’ that Gates was right about what he expected to be true. "

Squash 14 years ago

Just as a heads up, I cannot scroll to the bottom of your page. I keep bouncing as I hit the bottom and end up with 'Start using Squash' being cut in half. Screen res: 2560x1440

Regardless of the message the Microsoft is trying to deliver here they could at least make a website that does not make me close the tab in the first 10 seconds. What a mess.

I use an adblocker for everything. I do try to buy stuff from the stores of websites that I like to support them and encourage a revenue model that does not annoy me.

Very true, and if you want to be more specific my definition only works for finite duration continuous time signals with finite second moment. I use this definition as it also works well for understanding other transforms such as the Laplace transform.

You can also think of the Fourier Transform as a projection (dot product) of a signal onto the space of all sinusoids. That's the explanation that made everything click for me.