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tanszek:oktatas:techcomm:conditional_probability_and_information_theory

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tanszek:oktatas:techcomm:conditional_probability_and_information_theory [2025/11/05 12:06] – kissatanszek:oktatas:techcomm:conditional_probability_and_information_theory [2025/11/05 20:00] (current) – kissa
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 ===== Conditional Probability and Information Theory Exercises ===== ===== Conditional Probability and Information Theory Exercises =====
  
-  - What is the probability of rolling an odd number with a fair dice? How many bits of information does the statement $\text{"we roll an odd number with a fair dice"}$ contain? //(p=0.5; 1 bit)// \\ \\ +  - What is the probability of rolling an odd number with a fair dice? How many bits of information does the statement $\text{"we roll an odd number with a fair dice"}$ contain? //(p=0.5; I=1 bit)// \\ \\ 
   - We roll two physically identical dice. Let’s call event $A$ when we roll a 2 on either or both dice, and event $B$ when we roll a 3 on either or both dice. What is the probability of the event, when after rolling a 3, we immediately roll both a 2 and a 3 at the same time? (Rolling a 3 means that at least one die shows a 3.)  //(p=0.18)// \\ \\   - We roll two physically identical dice. Let’s call event $A$ when we roll a 2 on either or both dice, and event $B$ when we roll a 3 on either or both dice. What is the probability of the event, when after rolling a 3, we immediately roll both a 2 and a 3 at the same time? (Rolling a 3 means that at least one die shows a 3.)  //(p=0.18)// \\ \\
   - An urn contains 2 white and 2 black balls.   - An urn contains 2 white and 2 black balls.
-    - What is the probability of drawing two white balls consecutively without replacement? //(p=0.1666)//+    - What is the probability of drawing two white balls consecutively without replacement? //(0.17)//
     - How many bits of information does the statement $\text{"we draw 2 white balls consecutively without replacement from an urn containing 2 white and 2 black balls"}$ contain? //(2.58 bits)//     - How many bits of information does the statement $\text{"we draw 2 white balls consecutively without replacement from an urn containing 2 white and 2 black balls"}$ contain? //(2.58 bits)//
     - What is the entropy of this set of information (i.e., the average amount of information per news item)? //(1.25 bits)//     - What is the entropy of this set of information (i.e., the average amount of information per news item)? //(1.25 bits)//
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   - In a manufacturing process, the expected defect rate is 0.25. After producing 20 units, we randomly and simultaneously select 2 of them and inspect them:   - In a manufacturing process, the expected defect rate is 0.25. After producing 20 units, we randomly and simultaneously select 2 of them and inspect them:
     - How many bits of information has the news that $\text{"we selected 2 defective parts"}$ contain? //(4.24 bits)//     - How many bits of information has the news that $\text{"we selected 2 defective parts"}$ contain? //(4.24 bits)//
-    - How many elements does the news set have (what are the number of possible outcomes)? What is the entropy of the set? //(n=3; H=1.22 bits)// \\ \\+    - How many elements does the news set have (i.e., what are the number of possible outcomes)? What is the entropy of the set? //(n=3; H=1.22 bits)// \\ \\
   - In a communication system, we want to transmit 2-character symbolic words using the characters $A$, $B$, and $C$, with each word having equal probability, using a binary fixed-length code.   - In a communication system, we want to transmit 2-character symbolic words using the characters $A$, $B$, and $C$, with each word having equal probability, using a binary fixed-length code.
     - How many such symbolic code words can be formed? //(9)//     - How many such symbolic code words can be formed? //(9)//
     - What is the minimum number of bits needed for coding? //(4 bits)//     - What is the minimum number of bits needed for coding? //(4 bits)//
     - What is the average amount of information content for the words transmitted? //(3.17 bits)//     - What is the average amount of information content for the words transmitted? //(3.17 bits)//
-    - What is the redundancy of the code? //(0.2075)// \\ \\+    - What is the redundancy of the code? //(0.21)// \\ \\
tanszek/oktatas/techcomm/conditional_probability_and_information_theory.1762344392.txt.gz · Last modified: 2025/11/05 12:06 by kissa