Hi could i get help with this problem, attached as image:

Grades in a class are based on a linear combination of a final exam (worth 50% of the grade), a midterm (worth 30%), and homework (worth 20%). Let the random vector [F M H ]T consist of the final, midterm, and homework scores of a randomly picked student. Suppose the mean vector of [F M H ]T is [60 55 80]T and the covariance matrix is 121 80 10 80 144 15 10 15 9 Assume that the distribution of [F M H ]T is multivariate normal. a) Find the distribution of the student's overall score S = 0.5F + 0.3M + 0.2H. b) Before calculating the overall score, the instructor wonders whether F can just be predicted by a linear function of the random variable X = 0.3M + 0.2H. Find the least squares linear predictor of F based on X. c) Find the least squares predictor of F based on X. d) Find the root mean squared error of the predictor in Part c. e) Let Fm be F in standard units and let MS\" be M in standard units. Find the joint distribution of Fm and Ms". n Find Pu?\" > Mm + 0.5)