How to get variance for regression tree fit?

Suppose the true function is a tree such that:

$$f(x)=\sum_{j=1}^{J}b_j I(x \in R_j)+e_i$$ where $b_j=E(y|x \in R_j)$ ,$E(e_i)=0$ and $R_j$ as terminal node.

Suppose we got a fit for this tree via CART and cross validation so:

$$\hat{f}(x)=\sum_{j=1}^{\hat{J}}\hat{b_j}I(x \in \hat{R_j})$$

where $\hat{b}_j=sample\_avg(y_i|x_i \in \hat{R}_j)$

How could I get the variance of $\hat{f}(x)$ knowing $\hat{J}$, $\hat{b_j}$ and $\hat{R}_j$ as random variables?