Independent Random Variables: How to Prove Cov(X, Y) = 0

Independent Random Variables | Joint Distribution & Z = X + Y | VTU 1BMATCS301 Module 4 | Joint Probability Distribution In this video, you'll learn how to find the joint distribution of independent random variables, verify Cov(X, Y) = 0, and find the probability distribution of Z = X + Y — a must-know VTU 3rd Semester exam topic. APPLICABLE FOR VTU SUBJECT CODE: 1BMATCS301 – Module 4: Joint Probability Distribution PROBLEM SOLVED IN THIS VIDEO: X and Y are independent random variables. X takes values 2, 5, 7 with probabilities 1/2, 1/4, 1/4 respectively. Y takes values 3, 4, 5 with probabilities 1/3, 1/3, 1/3. a) Find the joint probability distribution of X and Y. b) Show that the covariance of X and Y is equal to zero. c) Find the probability distribution of Z = X + Y. PREVIOUS VIDEO: Independent Random Variables – Joint Distribution & Covariance    • How to Find Joint Distribution of Independ...   NEXT VIDEO IN THIS SERIES: Joint Distribution – Marginals, Covariance & Correlation    • Don't Miss This! Joint Distribution & Corr...   COMPLETE MODULE 4 PLAYLIST (Watch in Order):    • 1BMATCS301 Module 4 | Joint Probability Di...   OTHER MODULE PLAYLISTS (1BMATCS301 – 3rd Semester): Module 1 – Modular Arithmetic:    • 1BMATCS301 Module 1: Modular Arithmetic | ...   Module 2 – Statistics:    • 1BMATCS301 Module 2 | Statistics Complete ...   Module 3 – Probability Distributions:    • 1BMATCS301 Module 3 | Probability Distribu...   Module 3 (Updated) – Binomial, Poisson, Normal & Exponential:    • Probability Distributions | Binomial, Pois...   Module 5 – Statistical Inference:    • 1BMATCS301 Module 5 | Statistical Inferenc...   WHO IS THIS FOR? BE/B.Tech 3rd Semester students of VTU & Autonomous Colleges in Karnataka Subject Code: 1BMATCS301 CS branches: CSE, ISE, AIML, AI & DS, CSE (IoT), CSE (Cyber Security), Data Science, IT Students preparing for VTU internals, externals & backlog exams WHY WATCH THIS VIDEO? Step-by-step solutions for VTU exam problems Exam-focused VTU & Autonomous problems Simple, easy-to-understand method Covers repeated VTU exam questions Perfect for last-minute VTU revision STAY CONNECTED - Get All VTU Karnataka Maths Updates! WhatsApp Channel: https://whatsapp.com/channel/0029Vb6c... Telegram: https://t.me/vtumathswithmathematicst... Instagram: https://www.instagram.com/_mathematic... Subscribe & hit the bell icon so you never miss a video! If this video helped you, LIKE, SHARE with your VTU classmates, and COMMENT which problem you want next! #VTU #VTUKarnataka #1BMATCS301 #JointProbabilityDistribution #IndependentRandomVariables #Covariance #ZEqualsXPlusY #VTU2025 #VTU3rdSem #EngineeringMathematics #VTUMaths #VTU2025Scheme #VTUExams #VTUImportantQuestions #CSE #ISE #AIML #BETech #Autonomous