Probability distribution of particles created by a black hole

It has been demonstrated by Hawking that a spherical black hole formed by collapse will create particles, and that the average number of outgoing particles created in each mode satisfies a thermal distribution law. Recently, Wald has shown that the probability distribution of the number of outgoing particles in each mode, and not only the average number, obeys the thermal distribution law. In this paper, we give a simpler and more direct derivation of the blackbody probability distribution of the emitted particles.