Suppose that the expected values of ( x_1, x_2, x_3 ) are as follows:
( E(x_1) = θ_1 + θ_2 + θ_2 + ϵ_1 )
( E(x_2) = -θ_1 + θ_2 + θ_3 + ϵ_2 )
( E(x_3) = -2_ )
a) Find ( E(x_3) ) in terms of ( θ_1 ), ( θ_2 ), and ( θ_3 ).
b) Find the expected value of ( x_1 + x_2 + x_3 ).
c) Find the expected value of ( x_1 - x_2 ).
d) Find the expected value of ( x_1 ⋅ x_2 ).