Intuition for unequal variance of two very similar stopping times – math.stackexchange.com

I am learning about stochastic processes. Let $X_i \sim \mathrm{Bin}(1,\frac12)$ and independent $M$ and $N$ be the stopping times for the first Tail (i.e. $0$) and first Head (i.e. $1$). My task is ...