Continuous Random Variable | Probability Density Function | Find k, Probabilities & Variance |Solved

📘 Continuous Random Variable — PDF, Find k, Probability, Mean & Variance (Solved Problem) In this video, we solve an important Probability Density Function (PDF) problem step by step. Such questions are very common in VTU, B.Sc., B.E., B.Tech., and competitive exams. 🔢 Problem Covered in this Video (00:20): Find the constant k such that f(x) = kx² for x between 0 and 3 (excluding 0 and 3), f(x) = 0 otherwise, is a valid probability density function. Also compute: Probability that x is between 1 and 2 (excluding 1 and 2) Probability that x is less than or equal to 1 Probability that x is greater than 1 Mean of x Variance of x ✨ What You’ll Learn in This Video: ✔ How to find the constant k using the PDF normalization condition ✔ Step-by-step method to compute probabilities for intervals ✔ How to calculate mean and variance of a continuous random variable ✔ Tricks to solve PDF-based exam questions quickly ✔ Useful for VTU, B.Sc., B.E., B.Tech., and competitive exams 📌 Watch till the end for the complete solution with explanation. 📘 Probability Distributions – VTU BCS301 Module 1 🎥 Full Playlist (Autoplay all problems) https://www.youtube.com/playlist?list=PLM9RnGtTy9_-Xd_PmY1uXnHZ1LrXCB8N- 📌 Problems with Direct Links: 1️⃣ Coin & Die Problems – https://youtu.be/_8Zk8FuhDsE 2️⃣ Discrete Distribution (Mean & Var) – https://youtu.be/QqI7nJLrP0I 3️⃣ Find k, Mean & Std Dev – https://youtu.be/Kgd8qjBf-f8 4️⃣ Perished Apples Distribution – https://youtu.be/NBqEhyVK-T4 5️⃣ Probability Function (Find k & P(x)) – https://youtu.be/fPvW4izc0aM 6️⃣ Distribution P(x)=kx (Mean & Var) – https://youtu.be/JV0M3Sf4yRU 7️⃣ Binomial (Mean & Std Dev) – https://youtu.be/B_LgSxsYHZU 8️⃣ Binomial (Coin Toss & Def Pens) – https://youtu.be/UCJ7wN52lrw 9️⃣ Binomial (Def Lamps & Survival) – https://youtu.be/S62yQdSNAZ0 🔟 Binomial (Telephone & Quiz) – https://youtu.be/UX45WcMTyB4 1️⃣1️⃣ Poisson (Defectives in Samples) – https://youtu.be/iW4oBFDzAZ8 1️⃣2️⃣ Poisson (Students Test) – https://youtu.be/5LZGgkD5oF4 1️⃣3️⃣ Airline Seats & Families – https://youtu.be/8jb1RL-XnE0 1️⃣4️⃣ Fitting Binomial (Dice & Coins) – https://youtu.be/hfijBm3gREE 1️⃣5️⃣ Poisson (Mean & SD) – https://youtu.be/d7-z9y8CKp8 1️⃣6️⃣ Fit Poisson (Accidents Data) – https://youtu.be/fr84-j_c4f4 1️⃣7️⃣ Poisson (Blades & Fuses) – https://youtu.be/MjiEem7DmqY 1️⃣8️⃣ Poisson (Injection Reactions) – https://youtu.be/MZA0Str3wIE 1️⃣9️⃣ PDF f(x)=(x/6)+c – https://youtu.be/DwenlGtlEbw 2️⃣0️⃣ PDF f(x)=kx² (0 to 3)– https://youtu.be/H-xgw8JJkoc 2️⃣1️⃣ PDF f(x)=kx² [-3 to 3] – https://youtu.be/Ui91zRVvlaA 2️⃣2️⃣ PDF f(x)=kx·e^(-x) – https://youtu.be/9wRCZv4E1l8 2️⃣3️⃣ Exponential (Mean=3) – https://youtu.be/ZIJDFUmUW6k 2️⃣4️⃣ Exponential (Mean=5) – https://youtu.be/whINMS95qvk 2️⃣5️⃣ Exponential (Calls) – https://youtu.be/PZx5FZ_8N3M 2️⃣6️⃣ Exponential (Showers) – https://youtu.be/LXlkyEIfKGA 2️⃣7️⃣ Normal (Mean=30, SD=5) – https://youtu.be/tawEPP76zZg 2️⃣8️⃣ Normal (1000 Students Marks) – https://youtu.be/thmpqNzHy98 2️⃣9️⃣ Normal (Bulb Lifetime) – https://youtu.be/1VqRlWwn4QE 3️⃣0️⃣ Normal (Find Mean & SD) – https://youtu.be/xfXAB36pVGM 3️⃣1️⃣ Normal (Exam Marks) – https://youtu.be/7HOQD4roabU 💡 Support our work: 👉 https://www.youtube.com/channel/UC_OTtwh8_-q-bA7DoS--syg/join #ProbabilityDensityFunction #ContinuousRandomVariable #PDF #MeanAndVariance #StatisticsProblems #VTUExam #BScMaths #BTechMaths #ExamPreparation #MathsSolutions