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← 29-06 Variance_MLE

29-06 Variance_MLE

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Showing Revision 2 created 11/02/2015 by Udacity Robot.

  1. Now we talked about the easy thing, which is the mean.
  2. We're now going to move on to a much more challenging proof which is the σ².
  3. I once again started with the probability of data
  4. which is the very familiar product expression over here.
  5. And let me lay out the entire proof for you.
  6. As before, we start with the probability of data and as before we take the logarithm of it.
  7. And since I've already done this, I'll just restate what we previously derived.
  8. This would look familiar. If not, go back and watch the previous video.
  9. Now the key thing is that we take the derivative of spectral sigma.
  10. Let me lay out the entire proof for you. So here's how it looks.
  11. We take the logarithm this time with respect to sigma of all expression
  12. to arrive with this thing over here.
  13. We simplify this by multiplying something into here, factor out something over here,
  14. and we arrive at our desired result.
  15. Plug in those numbers as before.
  16. There's a total of 10 of those for seven open expressions on the left.