Assume we define a new random variable as X-g(9)-y2cos(0) with - . Analytically determine the PDF of the new variable . (x) as a functio of the as-of-yet unspecified PDF fo (0). . Plot x-g(0) to determine the roots. Show how the roots are determined. Use l. 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 s(8). A useful identity: sin(arccos(a))-VI-u, Assume we define a new random variable as X-g(9)-y2cos(0) with - . Analytically determine the PDF of the new variable . (x) as a functio of the as-of-yet unspecified PDF fo (0). . Plot x-g(0) to determine the roots. Show how the roots are determined. Use l. 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 s(8). A useful identity: sin(arccos(a))-VI-u