CS1 Gamma Distribution Explained from Scratch | Build Complete Understanding | Actuarial Science скачать в хорошем качестве

CS1 Gamma Distribution Explained from Scratch | Build Complete Understanding | Actuarial Science

CS1 Gamma Distribution Explained from Scratch | Build Complete Understanding | Actuarial Science Linkedin   / pratap-padhi   Website https://smearseducation.com/ Join my FREE Skool Community to get all updates and support https://www.skool.com/sme-education-9... Watch my previous recordinds on CS2 Time Series 👉    • Master Time Series Forecasting:Guide to AR...   CS2 Risk Modelling and Survival Analysis 👉   • Why One Random Variable Is Not Enough for ...   👉    • What is a Stochastic Process? Easy explana...   CS1 Previous recorded videos watch 👉    • CS1 Discrete Random Variables and Probabil...   CM1 Previous recorded videos watch 👉    • CM1 Simple Interest and Discount Explained...   👉    • CM1 Y Part2 Class1- A beginner's introduct...   TIMESTAMPS 00:00 Introduction to Gamma Function 00:06 Definition of Gamma Function 00:23 Why Gamma Function is Needed 01:46 Finding Gamma(1) 02:34 Finding Gamma(2) using Integration by Parts 05:39 General Pattern and Factorial Relation 06:45 Gamma Function Property and Factorial Link 10:43 Gamma Function for Non-Integer Values 12:27 Important Result Gamma(1/2) equals √π 13:13 Gamma Recursion Formula 16:29 Using Gamma Function for Fractional Values 19:20 Introduction to Gamma Distribution 21:11 Gamma Distribution Probability Density Function 27:59 Proof Gamma Distribution is a Valid PDF 45:33 Finding Expected Value of Gamma Distribution 50:07 Finding Second Moment E(X²) 52:53 Deriving Variance of Gamma Distribution 53:40 Exponential Distribution as Special Case DESCRIPTION In this CS1 Actuarial Science lecture, you learn Gamma Function and Gamma Distribution step by step with full mathematical explanation. This lecture covers the definition, properties, and practical use of the Gamma Function. You will see how Gamma Function connects factorials, exponential distribution, and continuous probability models. This lecture also proves Gamma Distribution is a valid probability density function and derives its mean and variance. Topics covered • Gamma function definition • Why Gamma function is needed • Gamma function values and properties • Gamma recursion formula • Gamma of integers and fractions • Gamma distribution PDF • Proof Gamma distribution is a valid PDF • Expected value of Gamma distribution • Variance of Gamma distribution • Exponential distribution as special case • Actuarial Science CS1 exam applications This lecture is essential for CS1 Actuarial Science students preparing for exams and interviews. This topic is heavily used in • Actuarial modeling • Risk modeling • Survival models • Insurance mathematics • Statistical inference #ActuarialScience #CS1 #GammaFunction #GammaDistribution #ProbabilityDistribution #ActuarialStudents #Statistics #Probability #ExponentialDistribution #ExpectedValue #Variance #IFoA #ActuarialExam #Mathematics #StatisticsLecture