  We study the moment-generating functions (MGF) for linear eigenvalue
statistics of Jacobi unitary, symplectic and orthogonal ensembles. By
expressing the MGF as Fredholm determinants of kernels of finite rank, we show
that the mean and variance of the suitably scaled linear statistics in these
Jacobi ensembles are related to the sine kernel in the bulk of the spectrum,
whereas they are related to the Bessel kernel at the (hard) edge of the
spectrum. The relation between the Jacobi symplectic/orthogonal ensemble
(JSE/JOE) and the Jacobi unitary ensemble (JUE) is also established.
