The total positivity of order two is a fundamental property
to investigate the sequential decision problem, and it also
plays an important role in the Bayesian learning procedure
for a partially observable Markov process. For this process,
we also deals with a job search, and observe the probability
densities on the state space after some additional transitions
by employing the optimal policy. This problem is considered
as an extension of a job search in a dynamic economy discussed
in Lippman and MacCall \cite{lip76e}, and we will investigate
a problem where the state changes according to a partially
observable Markov process. Associated to each state of the process,
the wages of a job is a random variable, and information about
the unobservable state is obtained through it. All information
are summarized by probability distributions on the state space,
and we employ the Bayes' theorem as a learning procedure.
By using a property called a total positive of order two,
some relationships among information, the optimal policy and
the probability density on the state space after some additional
transitions are obtained.