  We compute statistical properties of weak gravitational lensing by
large-scale structure in three Cold Dark Matter models. We use a P$^3$M
$N$-body code to simulate the formation and evolution of large-scale structure
in the universe. We perform $1.1\times10^7$ ray-tracing experiments for each
model using the multiple lens-plane algorithm. From the results of these
experiments, we calculate the probability distribution functions (PDF) of the
convergences, shears, and magnifications, and their root-mean-square (rms)
values. We find that the rms values of the convergence and shear agree with the
predictions of a nonlinear analytical model. We also find that the PDFs of the
magnifications $\mu$ have a peak at values slightly smaller than $\mu=1$, and
are strongly skewed toward large magnifications. In particular, for the
high-density model, a power-law tail appears in the magnification distribution
at large magnifications for sources at redshifts $z_s>2$. The rms values of the
magnifications essentially agree with the nonlinear analytical predictions for
sources at low redshift, but exceed these predictions for high redshift
sources, once the power-law tail appears.
  We study the effect of magnification bias on the luminosity functions of
high-redshift quasars, using the calculated PDFs of the magnifications. We show
that the magnification bias is moderate in the absence of the power-law tail in
the magnification distribution, but depends strongly on the value of the
density parameter. In presence of the power-law tail, the bias becomes
considerable, especially at the bright end of the luminosity functions.
