The following problem arises in molecular biology: The surface of a bacterium consists of several sites at which foreign molecules – some acceptable and some not – become attached. We consider a particular site and assume that molecules arrive at the site according to a Poisson process with parameter ?. Among these molecules a proportion p is acceptable. Unacceptable molecules stay at the site for a length of time which is exponentially distributed with parameter 1, whereas an acceptable molecule remains at the site for an exponential time with rate 2. An arriving molecule will become attached only if the site is free of other molecules. What percentage of time is the site occupied with an acceptable (unacceptable) molecule?Question: Consider a birth and death process X(t) with three states: 0 (unacceptable), 1 (free), and 2 (acceptable). Identify the birth rates and death rates. Find the stationary distribution ??