Approximate the expectation and the variance of a random variable using simulations. We are able to approximate the parameters of a random variable through simulations. For example, by sampling n values of a uniform variable, we can get the approximation of the expectation by averaging all the samples. Similarly, we can get a approximation to the variance. Your work in this lab assignment is to investigate the relationship between the approximation ratio and the sample quantity. As an example, consider a random variable with a normal distribution. Choose the parameters yourself. Then, generate 10, 100, 1,000, 10,000 samples.
For each sample set, compute its corresponding approximations to the expectation and the variance.
Plot one figure for expectation and one for variance to show the effect of different numbers of samples on the approximation ratio.