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1

Entropy does not depend on what the "labels" or values of the random variable is, it is a property ONLY of the distribution. After all you just use $P(x), P(y), P(x,y)$ etc in the formula not $x,y$. Once you realize this, the set of probabilities $P(x,y)$ is all you need to use and apply the original definition of entropy for a single random ...


3

First note that the the comma in the proability is the AND operator; $$ \Pr[X = x , Y = y] = \Pr[X = x \wedge Y = y]$$ This is common notation to simplify the writing. Now, explicitly write as $$p_i = \sum_{j=1}^{n} r_{ij} = \Pr[X = x_i \wedge Y = y_0] + \Pr[X = x_i \wedge Y = y_1] + \cdots + \Pr[X = x_i \wedge Y = y_m]$$ Since the random variables $X$ and $...


2

SecureRandom.getInstanceStrong() will ensure that a strong algorithm (securerandom.strongAlgorithms) will is used. It is available since Java version 8. Check your version before starting to use. If no such algorithm is available in running VM, it will throw NoSuchAlgorithmException. This failure is a better practice instead of defaulting into weak ...


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