Explain the memoryless property the exponential distribution (2 marks) f. State two limitations of Operations Research.

1. Memoryless Property of the Exponential Distribution:

The memoryless property of the exponential distribution is a unique characteristic that sets it apart from other probability distributions. This property states that the remaining time until an event occurs does not depend on how much time has already passed.

In mathematical terms, if X is a random variable that follows an exponential distribution, then the memoryless property can be expressed as:

P(X > s + t | X > s) = P(X > t)

This means that the probability that the event has not occurred by time s + t given that it has not occurred by time s is equal to the probability that the event has not occurred by time t. In other words, the distribution "forgets" all the past information.

2. Limitations of Operations Research:

a. Complexity: Operations research often involves complex mathematical models and algorithms. This complexity can make it difficult to understand and implement the solutions, especially for non-technical decision-makers.

b. Dependence on Accurate Data: The effectiveness of operations research is heavily dependent on the accuracy of the data used. If the data is inaccurate or incomplete, the solutions derived from operations research may not be reliable or applicable.

c. Time and Cost: Developing and implementing operations research models can be time-consuming and costly. This can be a significant limitation for small businesses or organizations with limited resources.

d. Assumptions: Operations research models often involve assumptions about the system being studied. If these assumptions are not valid, the results may not be applicable to the real-world system.