Self-information content, average information content, and mutual information content in information theory are all fundamental concepts for dealing quantitatively with the magnitude and significance of information.
First, the amount of self-information is a measure of how "surprising" an event is when it occurs, i.e., how much information it brings. For example, something that is certain to happen has no surprise and no information, but an event that is very rare is considered to contain a great deal of information. An event with a low probability of winning the lottery can be said to have a large amount of self-information by itself.
Next, the average information content, as the name implies, represents the average of the amount of self-information in multiple events. This is commonly referred to as "entropy" and measures how uncertain a given source of information is. The more diverse and unpredictable the outcome, like dice, the higher the entropy. On the other hand, a source of information that produces only the same result each time has no uncertainty and zero entropy.
And mutual information content is a measure of how much informational connection there is between two events. It is a measure of the "degree of association," that is, how much information can be obtained about one event by knowing about the other. For example, if knowing a symptom makes it easier to identify a disease, there is a large amount of mutual information between the symptom and the disease. On the other hand, if they are unrelated to each other, the amount of mutual information is zero, and knowledge of one has no effect on the other.
Thus, the self-information content represents individual surprise, the average information content represents overall uncertainty, and the mutual information content represents the relationship between the two variables, all of which play an important role in mathematically capturing the meaning of information.
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