2. Suppose an exam consists of an oral(R) and a written(W) component and R and W are correlated. Assume that E(R) = µr and V ar(R) = of , E(W) = Hw and Var (W) = ow. Let us assume that the total score T=0.5R+0.5W. | (a) Find an expression for E(T) in terms of µr and Hw. (b) Prove that Var (T) = 0.250ž + 0.25ow + 0.5Cov(R, W) . Where Cov(R, W) is the Covariance between R and W.

2. Suppose an exam consists of an oral(R) and a written(W) component and R and W are correlated. Assume that E(R) = µr and V ar(R) = of , E(W) = Hw and Var (W) = ow. Let us assume that the total score T=0.5R+0.5W. | (a) Find an expression for E(T) in terms of µr and Hw. (b) Prove that Var (T) = 0.250ž + 0.25ow + 0.5Cov(R, W) . Where Cov(R, W) is the Covariance between R and W.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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