The aim of this exercise is to show that -1ltpxylt1 for

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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

Reference no: EM13636429

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