2009/03/7

Is this true?

March 07th 2009 Posted to Uncategorized

So this thing on Wikipedia

http://en.wikipedia.org/wiki/Noisy-channel_coding_theorem

could have left it at the classical statement of the theorem with bullet #1. Then it goes on to say:

2. If a probability of bit error \(p_b\) is acceptable, rates up to \(R(p_b)\) are achievable, where

\(R(p_b) = \frac{C}{1-H_2(p_b)}\).

3. For any \(p_b\), rates greater than \(R(p_b)\) are not achievable.
(Read the article)

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2008/11/22

uniform by three

November 22nd 2008 Posted to Uncategorized

Here is a problem recently described to me. Apparently there is a more elegant solution (which may give more insight), but I don’t see it yet.

The problem: \(X, Y, Z\) are independent random variables uniformly distributed over [0,1]. What is the distribution of \((XY)^Z\)?
(Read the article)

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2006/10/24

What is this “blog”

October 24th 2006 Posted to Uncategorized

…you speak of… what, do I write to myself? I only have 100MB.

First post and already TeX can be rendered. I stole the idea from fakalin.

\( \int_{0}^{1}\frac{x^{4}\left( 1-x\right) ^{4}}{1+x^{2}}dx = \frac{22}{7}-\pi \)

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