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--- tanszek:oktatas:techcomm:statistical_properties [2025/09/30 05:27] – [Event Space] knehez
+++ tanszek:oktatas:techcomm:statistical_properties [2026/09/28 16:35] (current) – knehez
@@ Line 3: / Line 3: @@
 ==== Event Space ====
-The outcome of //experiments//, the //results of observations//, and the //status of systems// form a so-called '**event space**', where finite or infinite cardinality elementary events may occur. In probability theory, an __event space__ encompasses (includes) all possible outcomes of an experiment, such as flipping a coin, rolling a dice, or measuring the temperature of a system.
+The outcomes of //experiments//, the //results of observations//, and the //status of systems// form a so-called '**event space**', where elementary events of finite or infinite cardinality may occur. In probability theory, an __event space__ encompasses (includes) **all possible outcomes of an experiment**, such as flipping a coin, rolling a dice, or measuring the temperature of a system.
 These events may form sets. Because they can be sets, we may perform standard //set operations// (union, intersection, complements, etc.) on them.
@@ 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.
 $$ \lim_{k \to \infty} freq_i = \frac{k_i}{k} =  P(E_i) $$