Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 4

Описание: 📘 Mathematics-III (BCS301) – VTU 2023-24 | Module-2: Joint Probability Distributions & Markov Chain

In this video, we solve a Markov Chain problem to show that a given transition matrix is regular stochastic and to find its unique fixed probability vector (stationary distribution).
This topic belongs to Module-2 (Joint Probability Distributions & Markov Chain) as per the VTU syllabus for CS & Engineering and is useful for students of B.Sc, B.Tech, BE, and other universities studying Markov Chains.

🎯 Question (11th Video)
Show that the transition matrix

P = (0, 1, 0; 0, 0, 1; 1/2, 1/2, 0)

is a regular stochastic matrix. Also, find the associated unique fixed probability vector v = (x, y, z) such that vP = v and x + y + z = 1.
Marks: 7

▶ Watch here: 11th Video – Regular Stochastic Matrix & Fixed Probability Vector

🧮 Concepts Covered:

Markov Chain Transition Matrix

Regular Stochastic Matrix

Stationary / Fixed Probability Vector

Solving vP = v using linear equations

Normalization condition (sum of probabilities = 1)

Understanding uniqueness of stationary distribution

🎯 Playlist:
Joint Probability & Markov Chain | BCS301 – Module 2 | Mathematics-III | VTU 2023-24 | CS & Engineering
🔗    • Joint Probability & Markov Chain | BCS301 ...  

📺 Video Order for Continuous Learning:

1️⃣ Joint Probability Distribution - Pt.1 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.1 | Di...  

2️⃣ Joint Probability Distribution - Pt.2 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.2 | Di...  

3️⃣ Joint Probability Distribution - Pt.3 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.3 | Di...  

4️⃣ Joint Probability Distribution - Pt.4 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.4 | Di...  

5️⃣ Joint Probability Distribution - Pt.5 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.5 | Di...  

6️⃣ Joint Probability Distribution - Pt.6 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.6 | Di...  

7️⃣ Joint Probability Distribution - Pt.7 | Discrete Random Variables | Engineering Mathematics
   • Joint Probability Distribution - Pt.7 | Di...  

8️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 1
   • Unique Fixed Probability Vector for Regula...  

9️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 2
   • Unique Fixed Probability Vector for Regula...  

🔟 Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 3
   • Unique Fixed Probability Vector for Regula...  

1️⃣1️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 4
   • Unique Fixed Probability Vector for Regula...  

1️⃣2️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 5
   • Unique Fixed Probability Vector for Regula...  

1️⃣3️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 6
   • Unique Fixed Probability Vector for Regula...  

1️⃣4️⃣ Unique Fixed Probability Vector for Regular Stochastic Matrix: Example 7
   • Unique Fixed Probability Vector for Regula...  

1️⃣5️⃣ Markov Chain 01: Transition Probability Matrix with Examples | Engineering Mathematics

1️⃣6️⃣ Markov Chain Problem on Student Study Habits | Find Long Run Probability
   • Markov Chain Problem on Student Study Habi...  

1️⃣7️⃣ Markov Chain Problem on Smoking Habits | Find Long Run Probability
   • Markov Chain Problem on Smoking Habits | F...  

1️⃣8️⃣ Markov Chain Problem on Ball Throwing | Find Probabilities After 3 Throws
   • Markov Chain Problem on Ball Throwing | Fi...  

1️⃣9️⃣ Markov Chain Problem on Car Trading | Multi-Step Transition Probability
   • Markov Chain Problem on Car Trading | Mult...  

2️⃣0️⃣ Markov Chain Problem on Salesman’s City Visits | Find Long Run Probabilities
   • Markov Chain Problem on Salesman’s City Vi...  

2️⃣1️⃣ Markov Chain Problem on Three Boys Throwing a Ball | Find Probability After 3 Throws
   • Markov Chain Problem on Three Boys Throwin...  



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