Question about gamma distribution

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    Distribution Gamma
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SUMMARY

The discussion centers on calculating the expected number of observations from a gamma distribution within a specified interval. Given a gamma probability density function (pdf) characterized by an expected value E(y) of 1.5 and a variance var(y) of 0.75, the parameters can be derived as r = 2.25 and lambda = 1.5. To find the expected count of measurements in the interval (1.0, 2.5), one must compute 100 times the probability P(1 <= y <= 2.5) using the gamma pdf formula.

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semidevil
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so I don't even know where to start and how to approach this. suppose that a set of measurements y1, y2,...y100 were taken from a gamma pdf where E(y)= 1.5, and var(y) = .75. how many y(i's) would I expect to find in the interval (1.0, 2.5).

I have absolutely no idea where to start given my information.

so I know that gamma pdf = lamda^r / (r - 1)! * ye^(-lamda*y), for y > 0.

and i know the expected value formula and variance formula, e(y) = r/lamda and variance(y) = r/lamda^2.

but so what? what do I do?
 
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100*P(1<=y<=2.5)

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