swissgirl
  • swissgirl
Calculus: Find K
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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swissgirl
  • swissgirl
|dw:1353910548451:dw|
swissgirl
  • swissgirl
You need to use integration by parts
hartnn
  • hartnn
put u= -y^2/2 then.

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More answers

anonymous
  • anonymous
Is it:\[\int\limits\limits_{-\infty}^{\infty}ke^{-\frac{y^2}{2}}dy=1\]?
swissgirl
  • swissgirl
Yes
hartnn
  • hartnn
u= -y^2/2 find dy =... ?
swissgirl
  • swissgirl
I used u=y^2
swissgirl
  • swissgirl
but maybe its easier with u=-y^2/2
swissgirl
  • swissgirl
Its not smart to have that negative there
swissgirl
  • swissgirl
Do you agree?
swissgirl
  • swissgirl
@hartnn ?
hartnn
  • hartnn
oh, sorry.... yeah, its easier with e^u constants can be rearranged easily...
anonymous
  • anonymous
I got the wrong answer when evaluating the integral, and I won't do it again now. But this function is a gaussian, and it is expected that the constant k in this case has the value 1/sqrt(2pi)=sqrt(2pi)/2pi. That comes from the statistic theory.
swissgirl
  • swissgirl
ohhhhh
swissgirl
  • swissgirl
Yes the answer is 1/ sqrt(2*pi) I just so dont follow how they got that answer.
hartnn
  • hartnn
did u try that substitution and then integration by parts ?
swissgirl
  • swissgirl
I was getting weird answers. I have not really touched calculus for over a yr so i cld be messing up
hartnn
  • hartnn
\(\huge\int \frac{e^{-u}u^{-1/2}}{\sqrt2}du\) when 2u=y^2 yes, its messy...
swissgirl
  • swissgirl
How would you continue from here?
swissgirl
  • swissgirl
Can you show me?
swissgirl
  • swissgirl
ok dont show me
hartnn
  • hartnn
u need to know gamma function to solve that ... i am so sorry, my internet are giving me connection problems....
swissgirl
  • swissgirl
hmmm I know the gamma distribution function
swissgirl
  • swissgirl
ohhhh I see it now lol
hartnn
  • hartnn
\( \Gamma(z) = \int_0^\infty e^{-t} t^{z-1} dt \)
swissgirl
  • swissgirl
Yesssssss
hartnn
  • hartnn
now , you'll get it easily.
hartnn
  • hartnn
ask if u don't get...
swissgirl
  • swissgirl
Thanks let me try to work it out then. Thanks :)))))
swissgirl
  • swissgirl
what?
hartnn
  • hartnn
\(\Gamma{1/2} = \sqrt{\pi}\)
hartnn
  • hartnn
you'll need it.
swissgirl
  • swissgirl
ohhh coool never knew that
swissgirl
  • swissgirl
I feel like i am missing the basics in math :(
hartnn
  • hartnn
http://en.wikipedia.org/wiki/Gamma_function

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