Talk:Sighter Distribution

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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:

\(\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})\)

Huh?? Evidently the standard is to use variance not standard deviation. So the suggestion is wrong.
Herb (talk) 19:31, 31 May 2015 (EDT)

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


seems it should just be something like If \(C\) is the position of the true center relative to the experimental center \(C^*\) \((\overline{X}, \overline{Y})\), then the probability density function of \(C^*\) is:
\(PDF({C^*})= \)  yada yada

which would also require changing \(r_n\) to \(R_n\) in equation.

The proof takes σ as given and solves for the distribution as a function of σ and n. There is no sample σ involved in the proof. Yes, the Normal here is parameterized by variance, not standard deviation. If you want to rewrite the proof using a different notation for the distribution I guess you can give it a shot. David (talk) 21:03, 1 June 2015 (EDT)
I don't want just a different notation, I want consistency in the notation. The top part uses R(n) which gets swizzled to \(R_n\) in the lower part. That sort of thing drives me crazy. :-(
I'll fix this to my liking and then let you have a chance to throw up on it... :-)
Herb (talk) 23:31, 1 June 2015 (EDT)