1 Explain if the following equations are true or false If tr

1.( Explain if the following equations are true or false. If true, prove that or quote the right theorem with page number. If false, explain or give example.

(a)E[3X – 5Y] = 3E[X] – 5E[Y]

(b)Var[3X – 5Y] = 3Var[X] – 5Var[Y] for any two random variables X and Y

C. Var[3X – 5Y] = 3Var[X] – 5Var[Y] if X and Y are independent

(d)Cov[X, Y+Z] = Cov[X, Y] + Cov[X,Z]

Solution

b)http://www.ncssm.edu/courses/math/Talks/PDFS/Expected%20Value%20Thms.pdf

a) its wrong

d)http://banach.millersville.edu/~bob/book/Optimal/Solutions