Reduce variance with covariate adjustment

A covariate $X$ measured before the experiment accounts for 36% of the variance in outcome $Y$. a) Derive how CUPED/regression adjustment changes $\operatorname{Var}(\Delta)$ and quantify the expected sample-size savings. b) List the assumptions that would invalidate CUPED (e.g., post-treatment leakage, mis-timed covariates) and the diagnostics you would run. c) In this setting, would you choose stratified randomization or covariate adjustment, and why?

Overview: This question tests a data scientist's skill in experimental design, variance reduction techniques, and regression-based covariate adjustment (CUPED/ANCOVA) within randomized A/B tests, including understanding of statistical power and diagnostic checks.