(This article was first published on

**is.R()**, and kindly contributed to R-bloggers)The classic Pythagorean identity is: \(sin^2(\theta) + cos^2(\theta) =1 \)

The binomial formula which calculates the probability of obtaining k tails when flipping a coin n times, with a assumed probability p for each trial is: \( P(E) = {n \choose k} p^k (1-p)^{ n-k} \)

Finally, the normal (Gaussian) distribution defined by mean \(\mu\) and variance \(\sigma^2\) is:

\[f(x; \mu, \sigma^2) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2} (\frac{x-\mu}{\sigma})^2} \]

A video explaining this process can be found here:

http://www.youtube.com/watch?v=EaaLX_yQAM0

To

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