# Talk:Sighter Distribution

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

$$f_{R_n}(r_n)$$

seems it should just be something like If $$C$$ is the position of the true center relative to the experimental center $$C^*$$ $$(\overline{X}, \overline{Y})$$, 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)