PLEASE USE R AND R COMMANDER

5 . Use R commander to explore the distribution of the sample mean X when the variable of interest X follows an extremely skewed distribution. The data file "SampleMean Exponential" contains three columns: (1) Column 1 (x): 1,000 observations from an exponential distribution with mean 10 (rate=1/10=0.1). A histogram of this column approximates the shape of the population distribution. (2) Column 2 (xbar.n5): sample means of 1,000 samples of size n=5 generated from an exponential distribution with mean 10. A histogram of this column approximates the distribution of the sample mean X for samples of size n = 5. (3) Column 3 (xbar.n100): sample means of 1,000 samples of size n=100 generated from an exponential distribution with mean 10. A histogram of this column approximates the distribution of the sample mean X with sample size n = 100. a) Find the sample mean and sample standard deviation for each column (called the empirical results) and complete the following table. Please note that the standard deviation of an exponential distribution is the same as the mean. (6 marks) Mean Standard Deviation Theoretical Empirical Theoretical Empirical Shape Variable X (population) Y with n = 5 HI = OF = Right skewed He = X with n = 100 OF = Roughly Vn normal b) Draw a histogram for each column, and comment on the centre, spread (variation), and shape of the distributions. (6 marks)