Answer to Question #202257 in Statistics and Probability for RAGHAV SOOD

Question #202257

Suppose X is a gamma variate with E(x) = 3 and var(X ) = .7 Find the parameters 

α and λ of the gamma distribution.


1
Expert's answer
2021-06-03T14:02:12-0400

A random variable X which has the gamma distribution with a shape parameter "\\alpha" and a rate parameter "\\lambda" (i.e. "X\\sim \\Gamma (\\alpha ,\\lambda )" ) has the following mean and variance:


"E(X)=\\alpha\/\\lambda=3"




"Var(X)=\\alpha\/\\lambda^2=0.7"


Hence


"\\alpha=3\\lambda"




"\\dfrac{3\\lambda}{\\lambda^2}=0.7=>\\lambda=\\dfrac{30}{7}\\approx 4.2857"

"\\alpha=3\\lambda=\\dfrac{90}{7}\\approx 12.8571"



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