Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 2 / 12G / i / Solution

False. For probabilities $(0.4,0.2,0.2,0.1,0.1)$, first merge the two $0.1$ symbols. Subsequent ties allow Huffman trees with length multisets $(2,2,2,3,3)$ and $(1,3,3,3,3)$, both of expected length $2.2$.