1. ## [SOLVED] Help in checking my answer

The question goes like this:
Show how to use the chi-square distribution to calculate $\displaystyle P(a<S^2/\sigma^2<b)$

My solution:
$\displaystyle P(a<\frac{S^2}{\sigma^2}<b)$
=$\displaystyle P(a(n-1)<\frac{(n-1)S^2}{\sigma^2}<(n-1)b)$
=$\displaystyle P(an-a<\chi^2_{n-1}<nb-b)$

2. Originally Posted by noob mathematician
The question goes like this:
Show how to use the chi-square distribution to calculate $\displaystyle P(a<S^2/\sigma^2<b)$

My solution:
$\displaystyle P(a<\frac{S^2}{\sigma^2}<b)$
=$\displaystyle P(a(n-1)<\frac{(n-1)S^2}{\sigma^2}<(n-1)b)$
=$\displaystyle P(an-a<\chi^2_{n-1}<nb-b)$
Looks OK.

3. Originally Posted by noob mathematician
The question goes like this:
Show how to use the chi-square distribution to calculate $\displaystyle P(a<S^2/\sigma^2<b)$

My solution:
$\displaystyle P(a<\frac{S^2}{\sigma^2}<b)$
=$\displaystyle P(a(n-1)<\frac{(n-1)S^2}{\sigma^2}<(n-1)b)$
=$\displaystyle P(an-a<\chi^2_{n-1}<nb-b)$
You should justify the step from line two to line three.

CB