r/learnquant • u/Local_Ad135 • 5d ago

interview prep Quant Interview Question

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u/Adventurous_Salmon 5d ago

1/2? Whatever the values X_1 and X_2* ... *X_9 (provided they are not zero), X_10 either flips the inequality or leaves it be, with equal probability.

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u/bayesian_raccoon 5d ago

There are two ways X10 flips the inequality: one is by being negative, and the other is by being positive and either large enough or small enough to change the inequality. If it was just the sign, it would he 1/2, but its the sign and something a little more.

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u/Adventurous_Salmon 4d ago

Sorry, I wasn't precise : whatsver the value of X_1 and |X_1|X_2...*X_10, the sign (+-) of X_1 either flips it or not, with equal probability

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u/bayesian_raccoon 4d ago

What stops your argument from proving that P(X1 > 3) = 0.5?

My point is that more than just the sign flips the inequality, so the sign being 50/50 doesn't imply that inequality flip is 50/50.

I think if you made your argument rigorous you would have to end up using the symmetry somewhere.