1
vote
1answer
42 views

When is a minimum distance decoder also a maximum likelihood decoder?

It is well known that if we have a binary symmetric channel with crossover probability $\epsilon<0.5$ and we send a word $x$ through it, the most likely word is the one with minimum hamming ...
0
votes
1answer
65 views

A quick chanllenge: height and weight probability problem

The average height and weight of a group of people is 175cm and 70kg; Find the upper bound of the portion of the people who are over 200cm and over 100kg. I thought about Markov inequality, but I ...
0
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1answer
108 views

How to match a discrete distribution to a continuous distribution in information theoretic sense?

Let $$ S \sim N(\mu, \sigma^2) $$ be a normally distributed random variable with known $\mu$ and $\sigma^2$. Suppose, we observe $$ X = \begin{cases} T & \text{if $S \ge 0$}, \\ -T & ...
2
votes
1answer
190 views

Parameter estimation for a distribution by minimizing its conditional entropy

Let $X$ be a discrete random variable with Laplacian distribution with mean $0$ and scale $\lambda$, as $$ p(X) = \frac{1}{2\lambda} \exp\left(-\frac{|x|}{2\lambda}\right), \\ X \in ...