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1)X,Y are standard random variables, the correlation is 0.5. Given X, what's the conditional distribution of Y? 2)A,B,C are r.v.s. correlation between A and B is 0.9, between B and C is 0.9. is it possible that A is unrelated to C? 3)Given two assets, their average return, variance of return and correlation. Find a portfolio such that the sharpe ratio is optimal. 4)toss coins consecutively, get 1 pt if head is up and 2 pts if tail is up. So we can get a sequence of total points. Question: what is the probability that we have 100 pts in this sequence?
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Quantitative Research Associate

Interviewed at J.P. Morgan

3.9★
Nov 6, 2017

1)X,Y are standard random variables, the correlation is 0.5. Given X, what's the conditional distribution of Y? 2)A,B,C are r.v.s. correlation between A and B is 0.9, between B and C is 0.9. is it possible that A is unrelated to C? 3)Given two assets, their average return, variance of return and correlation. Find a portfolio such that the sharpe ratio is optimal. 4)toss coins consecutively, get 1 pt if head is up and 2 pts if tail is up. So we can get a sequence of total points. Question: what is the probability that we have 100 pts in this sequence?

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