Gamma function ( ) is defined by ( ) = x −1e−xdx. Gamma Distribution Variance. Gamma distribution, 2-distribution, Student t-distribution, Fisher F -distribution. Directly; Expanding the moment generation function; It is also known as the Expected value of Gamma Distribution. A Gamma random variable is a sum of squared normal random variables. Here, we will provide an introduction to the gamma distribution. In Chapters 6 and 11, we will discuss more properties of the gamma random variables. In the lecture entitled Chi-square distribution we have explained that a Chi-square random variable with degrees of freedom (integer) can be written as a sum of squares of independent normal random variables , ..., having mean and variance :. Gamma distribution. The gamma distribution is another widely used distribution. Its importance is largely due to its relation to exponential and normal distributions. Gamma Distribution Mean. There are two ways to determine the gamma distribution mean. It can be shown as follows: So, Variance = E[x 2] – [E(x 2)], where p = (E(x)) (Mean and Variance p(p+1) – p 2 = p Let us take two parameters > 0 and > 0. 0 If we divide both sides by ( ) we get 1 1 = x −1e −xdx = y e ydy 0 0

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