A step down means no arrival during service

Consider an M/G/1 queuing system with arrival rate $\lambda =1$ and independent and identically distributed successive service times having probability density function g(x) = xe⁻ˣ if x > 0, and 0 otherwise. Define, for $i=1,2,\dots ,I_i=1$ if the first transition is from i to i − 1, and $I_i=0$ if the first transition from i is i + 1. Then, $Var(I_2)$ equals