Geometric Interpretation on Chebyshev Type Inequalities

We present a geometric interpretation of Chebyshev type inequalities. This uses a simple diagram which illustrates the functional bound for the indicator function of the event whose probability we want to assess. We also give a geometric interpretation of the inequalities in terms of volume in a Euclidean space of appropriate dimension. Markov's inequality and Chebyshev's inequality are treated in more detail.