Derive the alternative expression for the covariance: Cov(X, Y ) = E[XY ] − E[X]E[Y ]. Hint: work out (X − E[X])(Y − E[Y ]) and use linearity of expectations. 2. Determine ρ  U, U 2   when U has a...

Derive the alternative expression for the covariance: Cov(X, Y ) = E[XY ] − E[X]E[Y ]. Hint: work out (X − E[X])(Y − E[Y ]) and use linearity of expectations.

2. Determine ρ  U, U²  when U has a U(0, a) distribution. Here a is a positive number.