Final answer:
The correct statement regarding simulation is that it is not typically used when an analytical solution is available. Simulations are useful tools for modeling complex systems which may include uncertainty in parameters and can manage both discrete and continuous random variables, providing insights where traditional methods might not be feasible.
Step-by-step explanation:
The correct statement about simulation is that it is not used when an analytical solution is available. This is a general rule because simulations are ideal when the system is too complex for analytical solutions, or when such solutions are not feasible due to system nonlinearity, or when there is inherent randomness that is difficult to capture analytically. However, the other statements about simulations are incorrect. Simulations can indeed be used with uncertainty in parameters; they can manage both discrete and continuous random variables, and rather than giving an exact optimal solution, they usually provide an approximation or a probabilistic understanding of the system behavior.
Simulations are useful for a variety of reasons. They help visualize complex relationships in ecosystems, address simple and complex systems, and can be more practical than both graphical and analytical methods. While analytical methods are more precise than graphical ones due to their reliance on mathematical calculations instead of drawing scale, simulations can sometimes offer insights when these methods are too cumbersome or impossible to use.
For example, simulations are often leveraged in cases like modeling biological systems where direct experimentation may not be possible or practical, and hence they can provide valuable predictions about the behavior of these systems. It's important to use a combination of simulations, observations, and experiments to achieve the most accurate models. Furthermore, scientists might opt for models because they are simpler to analyze, can yield more accurate results when reality is too complex, and they provide a reliable way to make predictions without the need for extensive computer calculations.