Let's calculate the mean and variance of the Gamma distribution. the probability density function of the Gamma distribution is defined to be

Let's calculate the mean and variance of the Gamma distribution. the probability density function of the Gamma distribution is dened to be i'zne'I fOI 2 2 0 331(3) : 11. D otherwise. In general, the mean of a continuous random variable is dened to be 00 E(X) :f :fn(2:) dz. 00 So, in the case ofthe gamma distribution this is 0 1 E00 : f joHle'Idz. 0 n. Usmg a well know result (see note below) we can easily calculate this to be EtX) :l In I The vanance can be calculate by 2 Venue : E((X 7 ENG) ), however it is much easier to calculate it using the alternative form 2 2 VaI(X) : E(X )7 E(_X) . The expectation of the X 2 is given by 00 1 E[X2] = / m"+29*1'd3. [3 11! Use the same result as before (see note below) we can easily calculate this to be 2 .. E[X ) :l in. Flom this we calculate that VartXJ : EIX2J M)2 :l In