Stratified sampling ratio with srswor The variable X under study have rectangular distribution with  interval (a,  a+ d ) the interval is divided into k equal subintervals which form k equal  strata of equals sizes . From each stratum simple random sample of n/ k units is drawn . Let V1 and V2 be the variance in estimator of population mean based on stratified and  simple random sampling of size n .
prove that  V1/V2 = 1/K²
My attempt
V2 = Var($\ y_R $ ) = $\ ( \frac{1}{n} - \frac{1}{\ k^2} ) \ S^2 $
As it is given in the question that total k stratum are of k subsamples in each of total population should be $\ k^2 $
V1 = Var($\ y_st $ ) = $\ ( \frac{1}{n} - \frac{1}{\ k^2} ) \sum_{i= 0 }^{k} \ p_i \ S_i^2 $
So v1/v2 = $\frac{\sum_{i=0}^{\ k} \ S_i^2 }{k \ S^2} $
Is this correct approach ??
Please  help if you know how to solve

The ratio of the variances depends on the ratio of the within-stratum variances of $X$  to the overall variance of $X$.  In this case, the stratum-specific variance for an interval of length $k$ is proportional to $1/k^2$ (specifically, it's $(b-a)/12k^2$)
