Gamma Distribution Homework: Estimating % Days > 10

EvLer
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Homework Statement


so, I'm given some sample data: electricity consumption on randomly selected n days, and asked to model the problem using Gamma distribution, then the question is to estimate percentage of days on which consumption was > 10 by using moment estimates.

So, I can find the moment estimates for the two parameters: alpha number of exponentially distributed RVs each with mean lambda.
But I do not know how to relate the estimates of the parameters to the question I am asked!
could someone explain, please?
 
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Really, you have to give the relevant formulas here to get more people (such as me) to try to help.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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