Estimating a Zero-Inflated Order-Arrival Model

Per-second order arrivals are modeled as follows: with probability $\pi$ the market is inactive and the observed count is exactly $0$; with probability $1-\pi$, the count is $\mathrm{Poisson}(\lambda)$.

From data, the empirical zero frequency is $0.70$ and the empirical mean count is $0.60$.

Use the method of moments to estimate $(\pi,\lambda)$.