Create a bivariate normal distribution with 200 samples whose mean is nu=[0,1] and the covariance matrix is Sigma=[[1,0.2],[0.2,2.]] [10] Plot the PDF of the samples. [10] Plot the PDF of the first variable and the second variable. [10] Calculate the correlation between the first X and the second random variable Y, and show their scattering plot. [10] Define a new random variable Z as Z=X+Y. What is the E[Z] and VAR[Z]. [10] Plot the PDF of Z. [10] Calculate the correlation and covariance between the first variable X and the new random variable Z, and show their scattering plot. [10] Interprept the calculated correlations and covariances between X&Y and X&Z.

Create a bivariate normal distribution with 200 samples whose mean is = [0, 1] and the covariance matrix is [10] Plot the PDF of the samples. = 1 02 0.2 2. (2) [10] Plot the PDF of the first variable and the second variable. [10] Calculate the correlation between the first X and the second random variable Y, and show their scattering plot. [10] Define a new random variable Z as Z = X + Y. What is the E[Z] and VAR[Z]. [10] Plot the PDF of Z. [10] Calculate the correlation and covariance between the first variable X and the new random variable Z, and show their scattering plot. [10] Interprept the calculated correlations and covariances between X & Y and X & Z.