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.