Comparison of Different Techniques to Generate Normal Random Variables∗

This exercise aims at exploring different techniques for creating a random variable X according to a normal distribution with zero mean and unit variance. The methods include the use of an inverse cumulative distribution function, the Box–Muller method, the polar technique and the application of the Central Limit Theorems to uniform random variables. The normal random variables generated by these methods are then compared according to different performance metrics, including their mean, variance and kurtosis, and conclusions are drawn about the performance of each of the techniques.