Consider the following model for the flow of water in and out of a dam. Suppose that, during day n, Y, units of water flow into the dam from outside sources such as rainfall and river flow At the end of each day water is released from the dam according to the following rule: If the water content of the dam is greater than

a, then the amount a is released. If it is less than or equal to

a, then the total contents of the dam are released. The capacity of the dam is C, and once at capacity any addi- tional water that attempts to enter the dam is assumed lost Thus, for instance, if the water level at the beginning of day n is x, then the level at the end of the day (before any water is released) is min(x + Y., C). Let S, denote the amount of water in the dam immediately after the water has been released at the end of day n. Assuming that the Y,, n1, are independent and identically distributed, show that {S,, n 1} is a random walk with reflecting barriers at 0 and Ca "