In the provided image, for variant 12, the table gives the probabilities $p(x_1), p(x_2), p(x_3), p(x_4), p(x_5), p(x_6)$ and the symbol durations $\tau_1, \tau_2, \tau_3, \tau_4, \tau_5, \tau_6$. For this specific variant:

• $p(x_1) = 0.14$

• $p(x_2) = 0.29$

• $p(x_3) = 0.27$

• $p(x_4) = 0.14$

• $p(x_5) = 0.04$

• $p(x_6) = 0.12$

• $\tau_1 = 0.2$ ms

• $\tau_2 = 0.1$ ms

• $\tau_3 = 0.5$ ms

• $\tau_4 = 1.5$ ms

• $\tau_5 = 7.3$ ms

• $\tau_6 = 4.8$ ms

To solve the problem of calculating entropy $H$, average duration $\tau$, productivity $H/\tau$, and redundancy $R$, we will proceed step by step.

1. Entropy $H$

The entropy formula is: $H = -\sum_{i=1}^{6} p(x_i) \log_2(p(x_i))$

2. Average Duration $\tau$

The average symbol duration is calculated as: $\tau = \sum_{i=1}^{6} p(x_i) \tau_i$

3. Productivity

Productivity is: $\text{Productivity} = \frac{H}{\tau}$

4. Redundancy

Redundancy is: $R = 1 - \frac{H}{\log_2 M}$ where $M = 6$ (the size of the alphabet).

I will now calculate these values.