In Matlab, do the following: a. Generate 500 random numbers from the pdf of X and 500 random numbers from the pdf of Y using the randn() function. Plot the histograms of these samples to verify that they are Gaussian with the correct mean and variance. b. Using the 500 samples from each pdf, generate the 500 samples for Z. Plot the histogram of Z to see if they agree with your answers from 1(a) and 1(b). c. Implement the ML estimates for the mean and variance you found in 1(c) and 1(d). It should take one or two lines of Matlab code. d. Now apply the estimators to compute the mean and variance of Z. How do the estimates compare to the theoretical mean and variance? e. Re-do parts (a)-(d) with 1000 samples. How would you compare the performance of the estimators with 500 and 1000 samples?

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In Matlab, do the following: a. Generate 500 random numbers from the pdf of X and 500 random numbers from the pdf of Yusing the randn() function. Plot the histograms of these samples to verify that they are Gaussian with the correct mean and variance. b. Using the 500 samples from each pdf, generate the 500 samples for Z. Plot the histogram of Z to see if they agree with your answers from 1(a) and 1(b). c. Implement the ML estimates for the mean and variance you found in 1(c) and 1(d). It should take one or two lines of Matlab code. d. Now apply the estimators to compute the mean and variance of Z. How do the estimates compare to the theoretical mean and variance? e. Re-do parts (a)-(d) with 1000 samples. How would you compare the performance of the estimators with 500 and 1000 samples? In Matlab, do the following: a. Generate 500 random numbers from the pdf of X and 500 random numbers from the pdf of Yusing the randn() function. Plot the histograms of these samples to verify that they are Gaussian with the correct mean and variance. b. Using the 500 samples from each pdf, generate the 500 samples for Z. Plot the histogram of Z to see if they agree with your answers from 1(a) and 1(b). c. Implement the ML estimates for the mean and variance you found in 1(c) and 1(d). It should take one or two lines of Matlab code. d. Now apply the estimators to compute the mean and variance of Z. How do the estimates compare to the theoretical mean and variance? e. Re-do parts (a)-(d) with 1000 samples. How would you compare the performance of the estimators with 500 and 1000 samples