Cnsider an exponentially distributed rv with a0 use the

Question

Part 1: generation of random numbers

a. Consider an exponentially distributed RV with a=0, use the inverse transform method to generate a sequence of exponentially distributed random numbers for different values of the parameter b. Plot the histograms and compare with the analytical probability density function (pdfs). See Sec. 3.5 in the textbook.

b. Repeat for a Weibull RV with a=1 and different values of the parameter b.

Part 2: Verification of the central limit theorem

- Use Matlab to verify the central limit theorem for the sum of N independent exponential RVs (with a=0 and b=1) for N=5, 10 and 20. Repeat for the sum of N independent Weibull RVs (with a=1 and b=4). Comment on the fit to the approximate Gaussian pdf.    

Part 3: Goodness of fit

- Use the appropriate measure(s) to compute the difference and to test the goodness of fit between the cdf/pdf of the sum of N independent exponential RVs and the approximate Gaussian cdf/pdf in Part 2. Repeat for the sum of the N independent Weibull RVs.  

Answer 1

In order to solve the following statistics numerical problems, apply the principles and laws of statistics and provide solutions to each part. Part 1: Generation of arbitrary numbers. a) Consider the exponentially distributed RV with a = 0, make use of the inverse transform method to create a series of exponentially distributed random numbers for various values of the parameter b. Plot the histograms and evaluate by means of the analytical probability density function (pdfs). b) Repeat for a Weibull RV having a = 1 and various values of the parameter b. Part 2: Verification of the central limit theorem Make use of Matlab to confirm the central limit theorem for the sum of N independent exponential RVs (having a=0 and b=1) for N=5, 10 and 20. Do again for the sum of N independent Weibull RVs (having a=1 and b=4). Remark on the fit to the approximate the Gaussian pdf.