Application of Cholesky decomposition (Matlab Programing) a) Write a program (cholprog.m) to find Cholesky decomposition of a symmetric positive definite matrix A Rnxn. Hint: Cholesky decomposition is A = LL", where L E Rnx" is a lower triangular matrix. b) We need to generate correlated random vectors, sampled from distribution N(u, E) for given mean u R and covariance matrix Rnxn. Write a program (corrNRV.m) to first generate M uncorrelated random vectors sampled from N(0,I) (using MATLAB command randn) followed by a procedure to generate y ~ N(u, 2) from &; ~ (0,1) for i {1,2..., M} by applying Cholesky decomposition on E. Note that this program is a widely used procedure to generate correlated random vectors from uncorrelated random vectors (not restricted to normal random vectors as well). For n = 2 and 3, write a program (Q2 2b.m) to plot 1000 uncorrelated random vectors sampled from N(0,1) and output correlated vectors for fixed p = 0 and covariance matrix & = 0.025 0.0075 0.001757 0.025 0.0075] 0.0075 0.007 0.00135 0.0075 0.007 (0.00175 0.00135 0.00043 Application of Cholesky decomposition (Matlab Programing) a) Write a program (cholprog.m) to find Cholesky decomposition of a symmetric positive definite matrix A Rnxn. Hint: Cholesky decomposition is A = LL", where L E Rnx" is a lower triangular matrix. b) We need to generate correlated random vectors, sampled from distribution N(u, E) for given mean u R and covariance matrix Rnxn. Write a program (corrNRV.m) to first generate M uncorrelated random vectors sampled from N(0,I) (using MATLAB command randn) followed by a procedure to generate y ~ N(u, 2) from &; ~ (0,1) for i {1,2..., M} by applying Cholesky decomposition on E. Note that this program is a widely used procedure to generate correlated random vectors from uncorrelated random vectors (not restricted to normal random vectors as well). For n = 2 and 3, write a program (Q2 2b.m) to plot 1000 uncorrelated random vectors sampled from N(0,1) and output correlated vectors for fixed p = 0 and covariance matrix & = 0.025 0.0075 0.001757 0.025 0.0075] 0.0075 0.007 0.00135 0.0075 0.007 (0.00175 0.00135 0.00043