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A nice grid form of calendar that illustrates matching birthdays. A drop-down and limited range of choice for the number of birthdays is given.
This page contains the definition of variance and higher moments using the expected value. It contains properties, with proofs, of variance, skew, and kurtosis.
Wikipedia entry for Markov's Inequality. It contains a statement and proof and notes that Chebyshev's inequality is a corollary.
Wikipedia entry for Chebyshev's Inequality. It contains statements and proofs for several forms. Also contains a discussion of ways to improve the bounds.
Wikipedia entry for Jensen's Inequality. It contains statements and proofs for several forms, and applications including for a probability density function.
A demonstration for two-dimensional random vectors of the Weak Law of Large Numbers. A circle represents the set of values within epsilon of the mean and a set of points is the random sample.
A video lecture proving that the correlation is less than one. It starts with finding the variance of \(aX + bY\), then sets \(b=1\) and finds the value of \(a\) that minimizes the variance.
This article gives a description of the Binomial Distribution. It has both graphic and functional forms of the cdf and pdf.
Quick demonstration of "collecting coupons." In this applet, we seek to match all six faces on a die, 42 mahjong tiles or 52 cards.
This is one in a series of lessons on probability from the Math Goodies site. The definition of conditional probability is given along with several examples from a variety of settings.