Question

В алфавите 4 буквы каждая выпадает с вероятностью 0,4 0,3 0,2 0,1. Найти общий объем информации

Answer 1

-1*[0,4*log_2(0,4)+0,3*log_2(0,3)+0,2*log_2(0,2)+0,1*log_2(0,1)]=log_2(0,4^0,4*0,3^0,3*0,2^0,2*0,1^0,1)*(-1)

читай комменты, такие дела, используй python:

0.4*math.log(1/0.4,2)+0.3*math.log(1/0.3,2)+0.2*math.log(1/0.2,2)+0.1*math.log(1/0.1,2)

ответ: 1,846 до 3 знаков после запятой.
1,8 бит

Answer 2

Calculating the total information

To calculate the total information (entropy) of an alphabet with 4 letters where each letter has a probability of occurring, we can use the Shannon entropy formula:

H = -p1log2p1 - p2log2p2 - p3log2p3 - p4log2p4

Where: - p1 is the probability of the first letter occurring, which is 0.4 - p2 is the probability of the second letter occurring, which is 0.3 - p3 is the probability of the third letter occurring, which is 0.2 - p4 is the probability of the fourth letter occurring, which is 0.1

Plugging these values into the formula:

H = -0.4log2(0.4) - 0.3log2(0.3) - 0.2log2(0.2) - 0.1log2(0.1) H = 1.5

Therefore, the total information or entropy of this alphabet is 1.5 bits.