Tagged Questions
0
votes
1answer
27 views
Easy bound involving logs and binomial coefficients
I am currently working on an information theory problem where I have to bound the divergence between two distributions.
The divergence can be simplified to:
$$\sum_{k=0}^N \ {N\choose k} ...
6
votes
0answers
67 views
Information-theoretic aspects of mathematical systems?
It occured to me that when you perform division in some algebraic system, such as $\frac a b = c$ in $\mathbb R$, the division itself represents a relation of sorts between $a$ and $b$, and once you ...
1
vote
1answer
55 views
Expression for the size of type class, or multinomial coefficient.
The notations follow those in Cover&Thomas, "Elements of Information Theory", 2ed.
I saw from a paper that the size of type class $T(P)$ can be expressed as
...
1
vote
1answer
52 views
generalization of base-n notation from naturals to fractions
not exactly sure how to best ask this. base-$n$ notation involves a series of digits written where each digit is a natural number less than $n$.
is there some math/theory generalization of ...
3
votes
1answer
63 views
How to guess a binary code with feedback
Suppose I want to guess a binary code, where the quality of my guess is provided by an evaluation function. I imagine a safe, where the user enters a binary code by flipping $N$ switches. After ...
2
votes
1answer
80 views
Intuition about the relation of combinations and entropy
It is not difficult to show that
$${n \choose \lambda n} \leq 2^{H(\lambda)n}$$
where $H$ is the binary entropy function:
$$H(\alpha) = -\alpha \lg \alpha - (1-\alpha)\lg (1-\alpha)$$
I was ...
1
vote
1answer
93 views
A Measure for Number of Unique N-Tuples
Suppose I have a multiset of numbers. I'm interested in the number of unique n-tuples that can exist using the numbers from this multiset. Now of course a closed form is of interest here, but what I'm ...
1
vote
1answer
212 views
How to calculate/approximate expectation of function of a binomial random variable?
I am stuck at following problem in my research.
Suppose that $M=m$ is a random variable with binomial distribution and parameters $n,p$. The constants $r$ and $\gamma$ are greater than zero. ...
13
votes
3answers
697 views
Expanding and understanding the poison pills riddle
You might have heard of the riddle that asks you to identify one fake pill (poisoned) among 12 pills of identical appearance, with the fake pill being either lighter or heavier than the others. You ...
