Solution
= Solution
A leaf at depth $d$ is reached with probability $2^{-d}$ and contributes $2^d$. Summing over leaves gives $\mathbb E[2^{X_1}]=\ell$. Since $L$ is the sample mean of the $2^{X_i}$, $\mathbb EL=\ell$.
= Solution
A leaf at depth $d$ is reached with probability $2^{-d}$ and contributes $2^d$. Summing over leaves gives $\mathbb E[2^{X_1}]=\ell$. Since $L$ is the sample mean of the $2^{X_i}$, $\mathbb EL=\ell$.