Three investments are available. The first pays fixed dividends of \(\$ 100\) at the times of a renewal process whose inter-renewal distribution is exponential with parameter \(1 / 5\). The second can pay either \(\$ 80, \$ 100\), or \(\$ 140\), each with probability \(1 / 3\), at the times of a renewal process whose inter-renewal distribution is \(\Gamma(2,4)\). The third pays an amount \(\$ 50 \cdot M_{i}\) at the deterministic times \(i=3,6,9, \ldots\), where each \(M_{i}\) has the Poisson distribution with parameter 1 , and the \(M_{i}\) 's are mutually independent. Which investment is preferable from the point of view of maximizing the long-run expected reward per unit time?