Distribution of sample means in a normally distributed population In a previous lab, we simulated sampling from a uniformly-distributed population - die rolls - and investigated the distribution of the sample means. Let's revisit the question of finding distributions of sample means. This time, we will investigate the means of samples that are drawn from a normally-distributed population. 1. Create a function called NormalMeans(n,m) that simulates taking n samples of size m from normally-distributed populations with mean 0 and standard deviation 1. Like the DiceMeans(n,m) function you created in Lab 6, this new function will compute (and keep track of) the sample mean for each of those n samples. Your function should return the following: - The mean of the n sample means - - The standard deviation of the n sample means An appropriately-named histogram of the n sample means (use the default bins) Run your function for n=10000 and for the following values of m: 1, 2, 10, 50, 100. Submit five outputs (five histograms, each with the means and standard deviations listed below). How do the means and standard deviations compare as m increases? How do the shapes of the graphs compare to one another? Distribution of sample means in an exponentially- distributed population Now, we will investigate the distributions of sample means of a very skewed population - one with an exponential distribution. 2. Create a function called ExponentialMeans(n,m) that simulates taking n samples of size m from exponentially-distributed populations with rate 1. As before, this new function will compute (and keep track of) the sample mean for each of those n samples. Your function should return the following: - The mean of the n sample means - The standard deviation of the n sample means - An appropriately-named histogram of the n sample means (use the default bins)