The coefficient of variation (CV) for a random sample $Y_1, ..., Y_n$ is defined by
$\qquad CV = \frac{S}{\bar{Y}}$,
where $S$ is the sample standard deviation and $\bar{Y}$ is the sample mean. CV measures the amount of
variation as a proportion of the sample mean. Suppose each $Y_i \sim N(0, \sigma^2)$ for $i = 1, ..., 10$.
(a) By using $F_{1, \nu} = t_{\nu}^2$, find the distribution of $10\bar{Y}^2 / S^2$ in terms of the F-distribution.
(b) Find the distribution of $S^2 / (10\bar{Y}^2)$.
(c) Using statistical tables, find the number $c$ such that
$\qquad Pr\left\{-c \le \frac{S}{\bar{Y}} \le c\right\} = .95$.
