l. Assume we define a new random variable as X g(0) V2cos(9) with . Analytically determine the PDF of the new variable /(x) as a function of the as-of-yet unspecified PDF fe () Plot x g() 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 fo(J). A useful identity: sin(arccos(l)-VI- 2. Using your general result for fr (x) as derived above, assume now that Determine an expression for Jx (x) for this particular and plot this function using MATLAB Analytically determine the mean and variance ofX using either the PDF (x) or . the Law of the Unconscious Statistician. Include this analvtic result in vour report l. Assume we define a new random variable as X g(0) V2cos(9) with . Analytically determine the PDF of the new variable /(x) as a function of the as-of-yet unspecified PDF fe () Plot x g() 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 fo(J). A useful identity: sin(arccos(l)-VI- 2. Using your general result for fr (x) as derived above, assume now that Determine an expression for Jx (x) for this particular and plot this function using MATLAB Analytically determine the mean and variance ofX using either the PDF (x) or . the Law of the Unconscious Statistician. Include this analvtic result in vour report