Discuss the two short comings of the mid-square method as generator of random numbers.(4 Marks)

The mid-square method for generating random numbers, while simple and easy to implement, has two main shortcomings:

1. Repeating Sequences: The most significant shortcoming of the mid-square method is the possibility of falling into short repeating cycles. If the method generates a number that has been previously generated, the sequence will start repeating from that point onward. This is particularly problematic if zero is generated, as the sequence will then only produce zeros.

2. Loss of Randomness with More Iterations: The mid-square method tends to lose randomness with more iterations. This is because the middle digits of the square of a number are not as random as the original number. As a result, the sequence of numbers generated by the mid-square method tends to become less random with each iteration.

These shortcomings limit the effectiveness of the mid-square method for generating truly random numbers, particularly for applications that require a large sequence of random numbers or a high degree of randomness.