Probability - u substitution to find gamma function.

sirhc1
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Homework Statement



\int_0^∞ x^2exp(-x/2) dx

Homework Equations



afe9f86ae39cdf0260aad124aac4a3e9.png


The Attempt at a Solution



Using u substitution:

u = x/2
du = 1/2 dx

\int_0^∞ 4u^2exp(-u) du*2
= 8 \Gamma(3)
= 8*3!
= 48

But the correct answer is 16 when I plug it in Wolfram's definite integral calculator. I don't see where's my mistake?

Thank you very much!
 
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Wow, Gamma(3) = 2!, not 3!. Silly me! Thanks anyways.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

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