we introduced 2 dif- Generating Gaussian Random Variables ferent algorithms to generating Gaussian random variables: (i)...

  

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we introduced 2 dif- Generating Gaussian Random Variables ferent algorithms to generating Gaussian random variables: (i) Inverse Method with approx- imated inverse CDF; and (ii) A-R Method using exponential as proposed distribution. (a) Implement the two methods in Python. (b) Verify your implementation as follows. Using your codes to generate 10,000 samples from the standard Gaussian distribution. Compare the histogram of the simulated data with the density of standard Gaussian. (c) Generate 100,000 samples using the two methods you have implemented and the function numpy.random. normal(), respectively. Compare their computation times. Can your implementation beat the numpy function? we introduced 2 dif- Generating Gaussian Random Variables ferent algorithms to generating Gaussian random variables: (i) Inverse Method with approx- imated inverse CDF; and (ii) A-R Method using exponential as proposed distribution. (a) Implement the two methods in Python. (b) Verify your implementation as follows. Using your codes to generate 10,000 samples from the standard Gaussian distribution. Compare the histogram of the simulated data with the density of standard Gaussian. (c) Generate 100,000 samples using the two methods you have implemented and the function numpy.random. normal(), respectively. Compare their computation times. Can your implementation beat the numpy function?

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