WRITE MATLAB PROGRAM PLEASE

Assignment: 1. Assume we define a new random variable as X-g(e) V2cos() with . Analytically determine the PDF of the new variable fX(x) as a function of the as-of-yet unspecified PDF fo (e) Plot x -g(e to determine the roots. Show how the roots are determined. Use MATLAB to graph the mapping function and indicate on the plot how the roots are found Derive an equation for the new PDF based as a function of the original PDF -la(9). A useful identity: sin(arccos()- * 1-2 2. Using your general result for f, (x) as derived above, assume now that Determine an expression for fx (x) for this particular and plot this function using MATLAB Analytically determine the mean and variance of X using either the PDF f (r) or the Law of the Unconscious Statistician. Include this analytic result in your report. 3. Generate a data record of at least 25000 uniformly distributed random numbers over the range- . Map this set of random numbers to a new set according to the function X-g(e) V2cos (0) Using a normalized histogram function, estimate the PDF f, (x) Using your sample mean and variance function, estimate the mean and variance of X. * Compare your estimated results with the theoretical quantities. * Assignment: 1. Assume we define a new random variable as X-g(e) V2cos() with . Analytically determine the PDF of the new variable fX(x) as a function of the as-of-yet unspecified PDF fo (e) Plot x -g(e to determine the roots. Show how the roots are determined. Use MATLAB to graph the mapping function and indicate on the plot how the roots are found Derive an equation for the new PDF based as a function of the original PDF -la(9). A useful identity: sin(arccos()- * 1-2 2. Using your general result for f, (x) as derived above, assume now that Determine an expression for fx (x) for this particular and plot this function using MATLAB Analytically determine the mean and variance of X using either the PDF f (r) or the Law of the Unconscious Statistician. Include this analytic result in your report. 3. Generate a data record of at least 25000 uniformly distributed random numbers over the range- . Map this set of random numbers to a new set according to the function X-g(e) V2cos (0) Using a normalized histogram function, estimate the PDF f, (x) Using your sample mean and variance function, estimate the mean and variance of X. * Compare your estimated results with the theoretical quantities. *