  The low energy properties of the spin-1/2 random Heisenberg chain with
ferromagnetic and antiferromagnetic interactions are studied by means of the
density matrix renormalization group (DMRG) and real space renormalization
group (RSRG) method for finite chains. The results of the two methods are
consistent with each other. The deviation of the gap distribution from that of
the random singlet phase and the formation of the large-spin state is observed
even for relatively small systems. For a small fraction of the ferromagnetic
bond, the effect of the crossover to the random singlet phase on the low
temperature susceptibility and specific heat is discussed. The crossover
concentration of the ferromagnetic bond is estimated from the numerical data.
