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Could someone explain why the the mean of the 20 independent observations from a unit exponential distribution (the sum of which has a gamma(20,1) distribution) has a gamma(20,20) distribution because I don't seem to understand why this is the case.

user12321
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  • Hint : Use the MGF – Vishaal Sudarsan Mar 23 '18 at 13:43
  • I have not been introduced to the calculation of MGFs which involves a sum of random variables – user12321 Mar 23 '18 at 14:03
  • The second parameter is presumably a rate parameter. The mean is $\frac1{20}$ of the sum, i.e. the mean has a rate $20$ times larger than the sum. This is just scaling – Henry Mar 23 '18 at 15:05
  • related: https://math.stackexchange.com/questions/2302101/why-is-the-sample-distribution-the-exponential-distribution-gamma-distributed – Henry Mar 23 '18 at 15:06

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