  We consider a particle moving in a one dimensional potential which has a
symmetric deterministic part and a quenched random part. We study analytically
the probability distributions of the local time (spent by the particle around
its mean value) and the occupation time (spent above its mean value) within an
observation time window of size t. The random part of the potential is same as
in the Sinai model, i.e., the potential itself is a random walk in space. In
the absence of the random potential, these distributions have three typical
asymptotic behaviors depending on whether the deterministic potential is
unstable, stable or flat. These asymptotic behaviors are shown to get
drastically modified when the random part of the potential is switched on
leading to the loss of self-averaging and wide sample to sample fluctuations.
