Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 224 / 3 / a

Table of contents
- Solution a

Solution

For feasible mass functions

Q_{1}, Q_{2}

at distortion levels

d_{1}, d_{2}

Q = λ Q_{1} + (1 - λ) Q_{2}

has nonzero-symbol mass at most

λ d_{1} + (1 - λ) d_{2}

. Concavity of information entropy gives

H (Q) \geq λ H (Q_{1}) + (1 - λ) H (Q_{2}) .

Taking maximizing sequences proves

ϕ (λ d_{1} + (1 - λ) d_{2}) \geq λ ϕ (d_{1}) + (1 - λ) ϕ (d_{2}) .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version