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Let X~gamma(2,1).

Find:

P(X>=2)
(X<=10)

I'm struggling to determine how to solve this. I know you must integrate some function from 2 to infinity and 0 to 10 but don't know what to integrate.

dpel
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Christopher
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  • I'm voting to close this question as off-topic because it is about probability and [math.se] instead of programming or software development. – Pang Mar 10 '17 at 01:18
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    I'm voting to close this question as off-topic because it is about probability and Mathematics instead of programming or software development. – Pac0 Jan 12 '18 at 22:47

1 Answers1

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There are actually two ways to define Gamma-distribution - one with scaling 'theta' and another with inverse scale 'beta', see https://en.wikipedia.org/wiki/Gamma_distribution

Fortunately, for parameter value of 1 there is no difference.

So you have to integrate PDF

f(x) = (1/G(2)) * x * exp(-x)

Gamma function at 2 is equal to 1. G(2)=1, so 

P(x) = S x exp(-x) dx

where S is integration notation.

P(x) = -(x+1)*exp(-x)

So now you have to substitute limits

Severin Pappadeux
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