24. Prove the Cauchy-Schwarz inequality, namely, that

$$

(E[XY])^2 ≤ E[X^2]E[Y^2]

$$

HINT: Unless Y = -X for some constant, in which case this inequality holds with equality, if follows that for all ????, 0 ≤ ????[(???? + ????)²] = ????[????²]² + 2????[????????] + ????[????²]
Hence the roots of the quadratic equation ????[????²]² + 2????[????????] + ????[????²] = 0 must be imaginary, which implies that the discriminant of this quadratic equation must be negative.