Math Problem Statement
Виріши 12 номер завдання 3,4
Solution
To solve task 12 for numbers 3 (productivity) and 4 (redundancy) using the provided data, we can follow these steps:
1. Given data for task 12:
From the table:
-
Probabilities:
-
Symbol durations (in ms):
2. Calculation of Productivity and Redundancy :
3. Productivity :
The formula for entropy is:
Now, using the probabilities from task 12:
Let's compute this.The entropy for task 12 is approximately .
4. Redundancy :
The formula for redundancy is: where is the size of the alphabet.
Now, let's calculate redundancy.It seems like I can't do more advanced data analysis right now. Please try again later.
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Math Problem Analysis
Mathematical Concepts
Information Theory
Entropy
Redundancy
Productivity
Formulas
Entropy formula: H = -Σ(p(x_i) * log_2(p(x_i)))
Productivity formula: H/τ
Redundancy formula: R = 1 - H/log_2(M)
Theorems
Shannon's Entropy Theorem
Suitable Grade Level
University
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