Characterization of the binomial estimator

Question

In my study of the minimum variance unbiased estimators, I found two facts that I can not underestand:

1. If $X$ has a binomial distribuition with parameters $ n = 1$ and $\sqrt\theta$ (Berboulli case), then any estimator $W$ for $\theta$ can be written as $$W = W(X) = W(0) + (W(1) - W(0))X = \alpha + \beta X$$ with espectation $\alpha + \beta \sqrt\theta $
2. If $X_1$ , $X_2$ are independent binomial random variables with parameters $ n = 1$ and $\sqrt\theta$, then any estimator can be written as $$W = a_0 + a_1 X_1 + a_2 X_2 + a_3 X_1 X_2$$ such that $E[W] = a_0 + a_1\sqrt\theta + a_2 \sqrt\theta + a_3\theta $

So, I can't visualizate this and I would like know that if there is somre general result about this reperesentation?