~ Uniform(0, 1). Let α be a positive integer. 1) Find E[Uα] and Var(Uα) 2) Find Cov(U, Uα) and Corr(U, Uα

A 6-sided die is rolled twice. Let X be the sum of the two rolls, Y be the first minus the second, and Z be the 5 times the first, minus the second. (a) Compute Cov(X, Y): Cov(X,Y) = (b) Compute Cov(X, Z): Cov(X, Z) =

Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.