Difference between revisions of "Talk:Sighter Distribution"
(kept fiddling with this.) |
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<math>f_{R_n}(r_n)</math> | <math>f_{R_n}(r_n)</math> | ||
− | seems it should just be | + | seems it should just be something like '''If <math>C^*</math> is the position of the true center relative to the experimental center <math>(\overline{X}, \overline{Y})</math>, then the probability density function of <math>C^*</math> is:<br />''' |
+ | <math>PDF({C^*})= </math> yada yada | ||
− | <math> | + | which would also require changing <math>r_n</math> to <math>R_n</math> in equation. |
− | |||
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[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 15:14, 30 May 2015 (EDT) | [[User:Herb|Herb]] ([[User talk:Herb|talk]]) 15:14, 30 May 2015 (EDT) |
Revision as of 14:03, 31 May 2015
I think there is some slop in the equations that needs fixing.
I think the second equation:
\(R(n) = \sqrt{\overline{x_i}^2 + \overline{y_i}^2}\)
should be:
\(R_n = \sqrt{\overline{X}^2 + \overline{Y}^2}\)
I think the third equation:
\(\bar X, \bar Y \sim N(0,\sigma^2/n)\)
should be:
\(\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})\)
There is another fine point that should be explicitly stated. The sample of three shots uses n as sample size. But the \(\sigma\) is the population standard deviation, not the sample standard deviation s.
Don't really like this
\(f_{R_n}(r_n)\)
seems it should just be something like If \(C^*\) is the position of the true center relative to the experimental center \((\overline{X}, \overline{Y})\), then the probability density function of \(C^*\) is:
\(PDF({C^*})= \) yada yada
which would also require changing \(r_n\) to \(R_n\) in equation.