Provide a transition probability matrix on the inventory level of this product at the start of each day, starting with 3 items.

Probability

The warehouse capacity of a given product is of 3 items at most. The daily demand for this product is given by the following probability distribution: p(0) = 0.3; p(1) =0.25, p(2)=0.25, p(3+)=0.2, where 3+ means 3 or more. When the remaining items at the end of a day are less than 2, an order is made at the start of the next day to replenish the level at 3 items (to be available at the start of the next day).

Provide a transition probability matrix on the inventory level of this product at the start of each day, starting with 3 items.