Geometric MOM estimator

Let $Y_1,Y_2,…,Y_n$ be i.i.d. discrete random variables from a population with probability mass function $$\mathbb{P}(Y=y;\theta)=\begin{cases}\theta(1-\theta)^y& \text{if }y\in\mathbb{N}\cup\{0\},\ 0& \text{otherwise,}\end{cases}$$ where $0<\theta\le 1$ is an unknown parameter. Assume the convention $0^0=1$. If $\hat\theta$ is the method of moments estimator of $\theta$, then which of the following statements is/are correct?