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Title: Information Volatility Speaker: M. Rao, University of Florida Time: 3:00pm‐4:00pm Place: ENG 4

As is well known the Shannon Entropy \(H(X)\) of a random variable \(X\) is by definition \(-\int_0^{\infty} f(x)\log f(x)\,dx\), which is the expectation of the random variable \(-\log f(X)\). In this talk we study its variance, which we call its Information Volatility (or \(\mathrm{IV}(X)\) for short). \(\mathrm{IV}(X)\) has some very good properties not shared by Shannon Entropy. For example, \(\mathrm{IV}(X)\) equaling zero characterizes the Uniform distribution; \(\mathrm{IV}(X)\) is invariant under the affine transformation; and has some convergence properties.