The aim of this exercise is to show that -1<=p(X,Y)<=1 for any pair (X,Y) of random variables, where p(X,Y) is the correlation coefficient
a) express f(t)=var(X+tY)=at^2+bt+c using the bilinearity of covariance
b) Why do we have b^2-4ac<=0? Hint: Quadratic Formula
c) Express p(X,Y) as a function of a,b,c and show that -1<=p(X,Y)<=1