  We show the emergence of a strongly interacting Bose-Fermi mixture from a
two-component Fermi mixture with population imbalance. By analyzing in situ
density profiles of $^6$Li atoms in the BCS-BEC crossover regime we identify a
critical interaction strength, beyond which all minority atoms pair up with
majority atoms, and form a Bose condensate. This is the regime where the system
can be effectively described as a boson-fermion mixture. We determine the
dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field
contributions. Our study realizes a Gedanken experiment of bosons immersed in a
Fermi sea of one of their constituents, revealing the composite nature of the
bosons.
