  We consider random transverse-field Ising spin chains and study the
magnetization and the energy-density profiles by numerically exact calculations
in rather large finite systems ($L\le 128$). Using different boundary
conditions (free, fixed and mixed) the numerical data collapse to scaling
functions, which are very accurately described by simple analytic expressions.
The average magnetization profiles satisfy the Fisher-de Gennes scaling
conjecture and the corresponding scaling functions are indistinguishable from
those predicted by conformal invariance.
