Institute of Information Science - University of Miskolc

Experience shows that the information value of certain news depends on their probability.

$$ I_{E_i} = f(P_i) $$

in which \( I_{E_i} \) means the information value. In this aspect the more unexpected or unlikely (rumour) a news is the bigger it's news value.

So the \(f\) function was selected according to Shannon's suggestion:

$$ I_E = log_2 \frac{1}{p_E} = -log_2( p_E ) [bit] $$

The properties of a logarithm function play an important role in the modeling procedure of the quantitative properties of a given information.

If an event space consist of two equal-probability event \(p(E_1) = p(E_2) = 0.5 \) then,

$$ I_{E_1} = I_{E_2} = log_2 \frac{1}{0.5} = - log_2 2 = 1 [bit] $$