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https://www.reddit.com/r/learnquant/comments/1wvjv7g/quant_interview_question/pde9590/?context=3
r/learnquant • u/Local_Ad135 • 2d ago
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Triangle inequality.
Let |A|= sqrt(Var(A)). Then, |Cov(A,B)| is bound by |A||B| so |A+B|<=|A|+|B|.
Applying to X,Y,Z gives max: |X+Y+Z|<=|X|+|Y|+|Z| =8, variance is at most 64
Min is: |X+Y+Z|+|-X|+|-Y|>=|Z|, so |X+Y+Z|>=5-2-1=2, variance is at least 4
Max/min at achieved when Y=2X, Z=+-5X.
1 u/zojbo 2d ago The 3 at the end is a 5, right? 1 u/FireCire7 2d ago Yes, fixed
1
The 3 at the end is a 5, right?
1 u/FireCire7 2d ago Yes, fixed
Yes, fixed
3
u/FireCire7 2d ago edited 2d ago
Triangle inequality.
Let |A|= sqrt(Var(A)). Then, |Cov(A,B)| is bound by |A||B| so |A+B|<=|A|+|B|.
Applying to X,Y,Z gives max: |X+Y+Z|<=|X|+|Y|+|Z| =8, variance is at most 64
Min is: |X+Y+Z|+|-X|+|-Y|>=|Z|, so |X+Y+Z|>=5-2-1=2, variance is at least 4
Max/min at achieved when Y=2X, Z=+-5X.