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--- tanszek:oktatas:techcomm:statistical_properties [2025/09/30 05:20] – [Frequency of Events] knehez
+++ tanszek:oktatas:techcomm:statistical_properties [2025/09/30 05:33] (current) – [Frequency of Events] knehez
@@ Line 7: / Line 7: @@
 These events may form sets. Because they can be sets, we may perform standard //set operations// (union, intersection, complements, etc.) on them.
-For example: the __union of two events__ in an experiment may represent the occurrence of either event, while the __intersection__ represents the simultaneous occurrence of both. When these operations occur, the event will carry information.
+For example: the __union of two events__ in an experiment may represent the //occurrence of either event//, while the __intersection__ represents the //simultaneous occurrence of both//. When these operations occur, the event will carry information.
 The __value of information__ related to these events can vary significantly based on everyday experience. For instance, knowing that a rare event has occurred (such as winning the lottery) typically provides more valuable information than learning about an event that occurs frequently or predictably.
@@ Line 19: / Line 19: @@
 In the \( E_i \) event space, an event happened \(k_i\) times then the frequency of that given event may be calculated with the following formula:
-$$ freq_i=\frac{k_i}{k} $$
+$$ freq_i=\frac{k_i}{k} = \frac{\text{number of favorable outcomes}}{\text{number of all possible outcomes}}$$
-This means that we divide the number of all events by the number (frequency) of that given event. In case of a large number of experiments this number will show us the probability of that event.
+This means that we divide the number of that //given event// by the number of all //experiments//. In the case of a large number of experiments, this number will show us the probability of that event.
 $$ \lim_{k \to \infty} freq_i = \frac{k_i}{k} =  P(E_i) $$