Chi-Square Distribution & Chi-Square Test | Example Problem 1 | Engineering Mathematics

🎓 In this video, we compute the Chi-Square statistic for the following frequency distribution (testing whether the die is fair) — perfect for VTU Mathematics-III (BCS301) – Module 4: Statistical Inference 2. Question: A die was thrown 264 times and the number appearing on the face xxx follows the frequency distribution: Faces (x): 1, 2, 3, 4, 5, 6 Frequencies (Observed OOO): 40, 32, 28, 58, 54, 60 You’ll learn: ✅ How to compute expected frequencies for equal-probability categories ✅ Step-by-step calculation of (O − E)² / E for each class ✅ Summation to get the Chi-Square statistic χ² ✅ How to interpret χ² (compare with critical value) to test fairness — VTU exam style 🎯 VTU Focus: Subject Code: BCS301 – Mathematics-III Module 4: Statistical Inference 2 Topics: Chi-Square Test, Goodness of Fit, Hypothesis Testing Useful for CS & Engineering students (2023–24 syllabus) 📚 Quick solution outline (shown step-by-step in the video) Chi-Square Distribution & Chi-Square Test | Statistical Inference | Full Concept & Solved Examples: https://www.youtube.com/playlist?list=PLM9RnGtTy9_90Yy40pvcUt8czAnW8l-T4 📘 Playlist Content: 1️⃣ Chi square distribution | Chi square test | Statistical inference | Part 1 🔗 https://youtu.be/j2msfQK9hsc 2️⃣ Chi square distribution | Chi square test | Statistical inference | Part 2 🔗 https://youtu.be/daoLth-Nq-s 3️⃣ Chi square distribution | Chi square test | Statistical inference | Part 3 🔗 https://youtu.be/oSr5qsNtZos 4️⃣ Chi square distribution | Chi square test | Statistical inference | Part 4 🔗 https://youtu.be/kBrCkoX6ErU 5️⃣ Chi square distribution | Chi square test | Statistical inference | Part 5 🔗 https://youtu.be/7FL4YOcsggM 6️⃣ Chi-Square Distribution & Chi-Square Test | Example Problem 1 | Engineering Mathematics 🔗 https://youtu.be/8ZBkUdVqBNY 7️⃣ Chi-Square Distribution & Chi-Square Test | Example Problem 2 | Engineering Mathematics 🔗 https://youtu.be/UXxh1KRGBHU 8️⃣ Chi-Square Distribution & Chi-Square Test | Example Problem 3 | Engineering Mathematics 🔗 https://youtu.be/DPGUQAeQuG8 9️⃣ Chi-Square Distribution & Chi-Square Test | Example Problem 4 | Engineering Mathematics 🔗 https://youtu.be/ShdsIUn3h_U 💎 Support Us: Join our channel and get access to exclusive perks 👇 🔗 https://www.youtube.com/channel/UC_OTtwh8_-q-bA7DoS--syg/join #ChiSquareTest #GoodnessOfFit #UnbiasedDie #StatisticalInference2 #VTUMathematics3 #BCS301 #HypothesisTesting #VTU #ProbabilityAndStatistics #Maths3VTU #VTUExamPreparation