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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.
Wikipedia entry for Jensen's Inequality. It contains statements and proofs for several forms, and applications including for a probability density function.
Wikipedia entry for Chebyshev's Inequality. It contains statements and proofs for several forms. Also contains a discussion of ways to improve the bounds.
This video lecture introduces covariance and proves several properties.
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 applet demonstrates an experiment consist[ing] of first tossing a coin, and then rolling a red die if the coin lands heads or a green die if the coin lands tails."

This applet simulates flipping a coin. The user can select the probability of a single coin flip landing with the heads side facing up. The user can set through the simulation or let it run.
This is a basic overview of the hypergeometric distribution with descriptions of expectation, variance, covariance, skewness, kurtosis, and hypergeometric function.
This lesson on the hypergeometric distribution includes notation, examples, calculator, and definitions. The material is written in a "student friendly" tone.
This applet demonstrating the hypergeometric distribution allows the user the choose $$N$$ number of squares (where $$N= 12,20,49$$, or $$51$$), and can select from $$K$$ number of objects to be c