The standard deviation of a random variable is the positive square root of its variance. Letting X

The standard deviation of a random variable is the positive square root of its variance. Letting σX and σY denote the standard deviations of the random variables X and Y, we define the correlation of X and Y by

(c) If σX+Y is the standard deviation of X +Y, show that

σX+Y ≤ σX +σY

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Cov(X, Y) Corr(X, Y) = (a) Starting with the inequality Var (X + X) 0, show that 1 Corr(X, Y). (b) Prove the inequality -1 Corr(X, Y) 1