Markov Chain Problem on Student Study Habits | Find Long Run Probability

Описание: 📘 Joint Probability Distributions & Markov Chain – Module 2

In this video, we solve a *Markov Chain* problem based on the study habits of a student.
We find the *long-run probability (steady-state probability)* that the student studies on a given night.
This problem helps understand the concept of *transition matrices, fixed probability vectors, and stationary distributions* in Markov Chains — useful for B.Sc, B.Tech, and B.E students from any university covering this topic.

🎯 Question:
A student's study habits are as follows:
If he studies one night, he is 70% sure *not* to study the next night.
If he does *not* study one night, he is 60% sure *not* to study the next night.
In the long run, how often does he study?

🧮 Concepts Covered:
Markov Chain transition matrix
Long-run (steady-state) probability
Fixed probability vector (π)
Regular stochastic matrix
Limiting behavior of Markov chains

🎯 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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