1. A shop has reopened after a long closure due to the pandemic. Before the pandemic, they found that their number of customers per day was modeled well by a $\mathrm{Pois}(\theta_0)$ distribution, with $\theta_0$ considered known (from years of experience). They wish to know whether customer levels are the same as what they were before the pandemic, so they decide to test $H_0: \theta = \theta_0$ vs. $H_1: \theta eq \theta_0$, based on observing i.i.d. $Y_1,Y_2,\dots,Y_n \sim \mathrm{Pois}(\theta)$, where $Y_j$ is the number of customers in the $j$th day after the reopening. Fix $\alpha = 0.05$ as the nominal Type I error rate. \medskip oin (a) Find the Wald test statistic. What is its exact distribution (give the PMF)