Prob & Stats, Lec 10B: Introduction to the Gamma, Exponential, & Chi-Square Distributions

   • Probability and Statistics Exam 1 Rev...  . The probability density function (PDF) for the continuous gamma distribution takes the form f(x)=c*x^(α-1)*e^(-x/β) for positive x and positive parameters α and β. The constant c must be solved for and it involves the Gamma function Γ(α), which is defined by an integral and, for positive integers n, has the property that Γ(n)=(n-1)! When α = 1, the PDF simplifies to f(x)=(1/β)*e^(-x/β), which is called an exponential distribution. When β = 2 and α = γ/2, then we call it a chi-square distribution with γ (little gamma) degrees of freedom. https://amzn.to/3rjDOoA (Probability and Statistics with Applications: A Problem Solving Text, by Asimow and Maxwell)

Calculus-based Probability and Statistics for Engineers and Scientists, Lecture 10, Part 2. Also for Data Science and Actuarial Science majors.

#ProbabilityAndStatistics #GammaDistribution #ExponentialDistribution #ChiSquare

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