b)The instructor wonders whether the final exam score

Fcan just be predicted by a linear function of the random variable=0.3+0.2

X=0.3M+0.2H. Find the least squares predictor of

Fbased on

X. Is it linear?

1. Predicting Scores [Your answers to this question should be decimal values or equations with numerical coefficients. For the arithmetic, you are welcome use the code cell at the end of the question. It's just there for your convenience we won't read it.] 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) The instructor wonders whether the final exam score F can just be predicted by a linear function of the random variable X = 0.3M + 0.2H. Find the least squares predictor of F based on X. Is it linear