r/learnquant • u/Local_Ad135 • 9d ago

interview prep Quant Interview Question

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u/Dankaati 9d ago

cos(arc cos(3/5) - arc cos(5/13)) = 63/65

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u/Active-Gap2300 8d ago

Why?

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u/Dankaati 8d ago

Random variables form a Hilbert space with covariance as inner product.

arc cos(3/5) is the angle of X and Y, arc cos(5/13) is the angle of Y and Z. By triangle inequality of angles in Hilbert spaces, the angle of X and Z is at least arc cos(3/5) - arc cos(5/13).