  The fluctuation-dissipation theorem together with the exact density response
spectrum for ideal quantum gases has been utilized to yield a new expression
for the static structure factor, which we use to derive exact analytical
expressions for the temperature{dependent pair distribution function g(r) of
the ideal gases. The plots of bosonic and fermionic g(r) display "Bose pile"
and "Fermi hole" typically akin to bunching and antibunching as observed
experimentally for ultracold atomic gases. The behavior of spin-scaled pair
correlation for fermions is almost featureless but bosons show a rich structure
including long-range correlations near T_c. The coherent state at T=0 shows no
correlation at all, just like single-mode lasers. The depicted decreasing trend
in correlation with decrease in temperature for T < T_c should be observable in
accurate experiments.
