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If $g$ is a function of the random variable $X$, is it true that $H(X) = H(X) + H(g(X)\mid X)$?

I think my homework about entropy is formulated incorrectly.

The question is the following:

let $X$ be a discrete random variable. Show that the entropy of a function $g$ of $X$ is less than or equal to the entropy of $X$ by justifying the following steps:

125 more words

If $g$ is a function of the random variable $X$, is it true that $H(X) = H(X) + H(g(X)\mid X)$?

I think my homework about entropy is formulated incorrectly.

The question is the following:

let $X$ be a discrete random variable. Show that the entropy of a function $g$ of $X$ is less than or equal to the entropy of $X$ by justifying the following steps:

125 more words

If $g$ is a function of the random variable $X$, is it true that $H(X) = H(X) + H(g(X)\mid X)$?

I think my homework about entropy is formulated incorrectly.

The question is the following:

let $X$ be a discrete random variable. Show that the entropy of a function $g$ of $X$ is less than or equal to the entropy of $X$ by justifying the following steps:

125 more words

If $g$ is a function of the random variable $X$, is it true that $H(X) = H(X) + H(g(X)|X)$?

I think my homework about entropy is formulated incorrectly.

The question is the following:

let $X$ be a discrete random variable. Show that the entropy of a function $g$ of $X$ is less than or equal to the entropy of $X$ by justifying the following steps:

107 more words

Fun problem. Apparently $\prod_i(1-p_i) \geq 1 - \sum_ip_i$ with $p_i \in [0,1]$ is always true. But how to demonstrate it?

so, I want to demonstrate the validity of the following inequality:

$$
\prod_i(1-p_i) \geq 1 – \sum_ip_i
$$

with $p_i \in $, it is always true, which it seems to be always the case if you test it with some random numbers. 203 more words