Question 5 and correlation coefficient Here we will simulate the random variables for their covariance and...

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Question 5 and correlation coefficient Here we will simulate the random variables for their covariance and correlation coefficient. We will also learn how to generate correlated random variables for a given correlation coef- ficient. (a) Generate two standard Gaussian random variables for 100.000 samples. Make sure you generate the random variables correctly by checking their means and variances. (b) Matlab Simulations - Numerical calculation for covariance Through your simulation data, determine the covariance and the correlation coefficient between the generated data. Compare your values with Matlab's cov and corrcoef functions and observe that they agree, or the functions available from the libraries of your programming platform. We assume that Matlab or your random variable generator generates uncorrelated values. Hence, you should observe that the covariance and correlation coefficient to be close to zero. (c) One way to introduce correlation between to random variables, X₁ and X₂ is to generate a new normal random variable, X3 with zero mean and 1-p² variance, i.e. X3 (0,1-p²), and then modifying X₁ as X₁ = p.X₂ + X3 where p is the correlation coefficient. Modify X₁ according to the above formula so that the correlation coefficient between X₁ and X₂ is p. Verify this by using Matlab's corrcoef function. (d) Now generalize the above approach and introduce 0.7 correlation coefficient for two normal random variables with μ₁ = 3, o=3 and p2 = 10, 0 =5. Verify your implementation by checking the means, variances, and correlation coefficient between the random variables, X₁ and X₂. Question 5 and correlation coefficient Here we will simulate the random variables for their covariance and correlation coefficient. We will also learn how to generate correlated random variables for a given correlation coef- ficient. (a) Generate two standard Gaussian random variables for 100.000 samples. Make sure you generate the random variables correctly by checking their means and variances. (b) Matlab Simulations - Numerical calculation for covariance Through your simulation data, determine the covariance and the correlation coefficient between the generated data. Compare your values with Matlab's cov and corrcoef functions and observe that they agree, or the functions available from the libraries of your programming platform. We assume that Matlab or your random variable generator generates uncorrelated values. Hence, you should observe that the covariance and correlation coefficient to be close to zero. (c) One way to introduce correlation between to random variables, X₁ and X₂ is to generate a new normal random variable, X3 with zero mean and 1-p² variance, i.e. X3 (0,1-p²), and then modifying X₁ as X₁ = p.X₂ + X3 where p is the correlation coefficient. Modify X₁ according to the above formula so that the correlation coefficient between X₁ and X₂ is p. Verify this by using Matlab's corrcoef function. (d) Now generalize the above approach and introduce 0.7 correlation coefficient for two normal random variables with μ₁ = 3, o=3 and p2 = 10, 0 =5. Verify your implementation by checking the means, variances, and correlation coefficient between the random variables, X₁ and X₂.

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Here are the stepbystep workings for each part of the question a 1 Generate N 100000 standard normal random variables for X1 X1 normrnd01N1 2 Generate ... View the full answer