4. In class, we saw that the Central Limit Theorem applies to sample means. In this problem,let's show that it also applies to sample sums. a. Use the m-file named “CLT_sample_sum” posted on Canvas to build the probabilitydistribution from Problem 2. Determine the mean and variance of this PDF. b. Let's define an “experiment” as randomly selecting 1,000 “measurements” from the distribution. Use the "random" function in MATLAB to draw 1,000 random numbers from this distribution. Generate a histogram of the data with 20 bins. Notice how the shape of the histogram is similar to the PDF from which the data was drawn. c. Now perform 10,000 experiments (with 1,000 measurements each). For each experiment, sum the measurements. Generate a histogram of the sample sums with 50 bins. Notice how the shape of the histogram of sample sums looks like a normal distribution. d. Fit a normal distribution to the histogram of sample sums from part (c). What are the mean and variance of the fitted normal distribution? How do these values compare to the mean and variance of the original PDF from part (a)?