Let X Y Z Where Y And Z Are Nonnegative Random Variables Such That Yz 0 A Show T

Let X = Y-Z where Y and Z are nonnegative random variables such that YZ = 0(a) show that Cov(Y,Z) <=0(b) show that var(X)=> var(Y) + var(Z)(c) Use the result of part (b) to show that var(x) >= var(max{0,X}) + var(max{0,-X})