The variance risk premium in a two-state economy

Over the next month the economy is either calm (probability 0.9) or in crisis (probability 0.1). Annualised realised variance is 0.01 (10% vol) in calm and 0.16 (40% vol) in crisis. The stochastic discount factor is $M=0.9$ in calm and $M=2.0$ in crisis. (a) Compute $E^{\mathbb P}[RV]$, $E^{\mathbb Q}[RV]$ and the variance risk premium in variance units, and the corresponding "implied" and "expected realised" vols. (b) Verify Proposition 9.7 by computing $\operatorname{Cov}(M,RV)/E[M]$. (c) A trader sells one unit of variance notional at the fair strike every month. What is her expected P&L per month under $\mathbb P$, her P&L in a crisis month, and the probability she loses in a given month?