b$)$ Show that the variance of the mean of a systematic sample is given by:

Var$(\frac{?}{\text{b}\text{a}\text{r}}(y{)}_{st})=\frac{N-1}{N}{S}^2-\frac{k(n-1)}{N}{S}_{wsy}^2$

Where $S_{wsy}^2=\frac{1}{k(n-1)}{\displaystyle \underset{i=1}{\overset{k}{}}}(y_i-(\frac{?}{\text{b}\text{a}\text{r}}(y)){)}^2$ is the variance among the units that are within the same

systematic sample?