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--- tanszek:oktatas:techcomm:statistical_properties [2025/09/30 04:40] – [Event Space] knehez
+++ tanszek:oktatas:techcomm:statistical_properties [2025/09/30 05:33] (current) – [Frequency of Events] knehez
@@ Line 1: / Line 1: @@
-====== Statistical properties ======
+====== Statistical properties of Information ======
 ==== Event Space ====
@@ 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.
 $$ \lim_{k \to \infty} freq_i = \frac{k_i}{k} =  P(E_i) $$
@@ Line 35: / Line 35: @@
 {{:tanszek:oktatas:techcomm:pasted:20240826-164556.png}}
-The probability of every event will be 1/6 which can be calculated with the following formula. The rolls (of the dice) will form a so-called //full event system//. In the case of a //full event system// the sum of the probabilities (of each event) is 1 (by definition).
+The probability of every event will be \(\frac{1}{6}\), which can be calculated with the following formula. The rolls (of the dice) will form a so-called //full event system//. In the case of a //full event system// the sum of the probabilities (of each event) is 1 (by definition).
 If one of the events happens then the others can not happen:
@@ Line 81: / Line 81: @@
 Create sets containing all the possibilities.
-Try the following c code here: https://www.onlinegdb.com/online_c_compiler and examine the results.
+Try the following c code here: [[https://www.onlinegdb.com/online_c_compiler| online compiler]] and examine the results.
 <sxh c>
@@ Line 88: / Line 88: @@
 #include <time.h>
-#define SIMULATIONS 1000
+#define SIMULATIONS 10000
 // Function to simulate the birth of twins
@@ Line 114: / Line 114: @@
     // Calculate and print the result
-    double probability = (double)at_least_one_girl / SIMULATIONS * 100;
+    float probability = (float)at_least_one_girl / SIMULATIONS;
-    printf("In %.2f%% of cases, there is at least one girl in the twin pair.\n", probability);
+    printf("In %.2f%% of cases, there is at least one girl in the twin pair.\n", probability * 100.0f);
     return 0;