**Python Language

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Programming Problem Modify your previous lab to do the following: 1. Generate the raw data, PDF and CDF for W = X + Y where X Gaussian (0, 100) and Y Gaussian (0, 100). Compute the mean and variance of W. 2. Generate the raw data, PDF and CDF for W = X + Ywhere X Gaussian (10, 100) and Y Gaussian (20, 100). Compute the mean and variance of W. 3. Generate the raw data, PDF and CDF for W = X+ X2 + X3 + X + Xs where X; Gaussian (10, 100). Compute the mean and variance of W. Central Limit Stuff 4. Generate the raw data, PDF and CDF for W = + + x3 + Xe + X, where X; Uniform (0, 10). Compute the mean and variance of W. a+b and Var[Xi] = (b-a) 12 E[Xi] = 2 5. Generate the raw data, PMF and CDF for W = X2 + X2 + x3 + X4 + X, where X; Binomial (10,0.5). Compute the mean and variance of W. E[/i] = np and Var[/i] = np(1-p) 6. Generate the raw data, PMF and CDF for W = X2 + X2 + X2 + X4 + X, where X;" Geometric (0.5). Compute the mean and variance of W. (1-P) E[Xi] = and Var[Xi] = p 1 7. Generate the raw data, PMF and CDF for W = X2 + ... + Xo where XGeometric (0.5). Compute the mean and variance of W. Programming Problem Modify your previous lab to do the following: 1. Generate the raw data, PDF and CDF for W = X + Y where X Gaussian (0, 100) and Y Gaussian (0, 100). Compute the mean and variance of W. 2. Generate the raw data, PDF and CDF for W = X + Ywhere X Gaussian (10, 100) and Y Gaussian (20, 100). Compute the mean and variance of W. 3. Generate the raw data, PDF and CDF for W = X+ X2 + X3 + X + Xs where X; Gaussian (10, 100). Compute the mean and variance of W. Central Limit Stuff 4. Generate the raw data, PDF and CDF for W = + + x3 + Xe + X, where X; Uniform (0, 10). Compute the mean and variance of W. a+b and Var[Xi] = (b-a) 12 E[Xi] = 2 5. Generate the raw data, PMF and CDF for W = X2 + X2 + x3 + X4 + X, where X; Binomial (10,0.5). Compute the mean and variance of W. E[/i] = np and Var[/i] = np(1-p) 6. Generate the raw data, PMF and CDF for W = X2 + X2 + X2 + X4 + X, where X;" Geometric (0.5). Compute the mean and variance of W. (1-P) E[Xi] = and Var[Xi] = p 1 7. Generate the raw data, PMF and CDF for W = X2 + ... + Xo where XGeometric (0.5). Compute the mean and variance of W