Information Loss in Deterministic Signal Processing Systems by Bernhard C. Geiger & Gernot Kubin

Author:Bernhard C. Geiger & Gernot Kubin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Problem 2

We know from Proposition 4.1 that for X and Y independent,

Give examples where the left, the right, and both inequalities are strict. Hint: You can focus on (multivariate) Gaussian RVs that are supported on a lower-dimensional subspace of .

Problem 3

In Example 18 we claimed that if X and N are independent. Show this rigorously! Hint: Suppose that exists and is finite -a.s. and make use of the first property of Proposition 4.1.

Problem 4

Information dimension of the Cantor distribution. Consider the following sets:

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