In each case show that the statement is true or give an example showing that it is false.
(a) If {X, Y} is independent, then {X, Y, X + Y} is independent.
(b) If {X, Y, Z} is independent, then {Y, Z} is independent.
(c) If [Y, Z) is dependent, then {X, Y, Z] is dependent.
(d) If all of X1, X2,..., Xk are nonzero, then [X1, X2,..., Xk) is independent.
(e) If one of X1, X2,..., Xk is zero, then {X1, X2,..., Xk} is dependent.
(f) lf aX+ bY+ cZ = 0, then {X,Y,Z} is independent.
(g) If {X, F, Z} is independent, then aX + bY + cZ = 0 for some a, b, and c in R.
(h) If {X1,X2,...,Xk}is dependent, then t1X1 + t2X2 + ∙ ∙ ∙+ tkXk = 0 for some numbers t, in R not all zero.
(i) If {X1, X2,..., Xk} is independent, then t1X1 + t2X2 +∙ ∙ ∙ + tkXk = 0 for some ti, in R.