Interview Question: Back to Normal

Sample Question #6 (statistics)

Random variable X is distributed as N(a, b), and random variable Y is distributed as N(c, d). What is the distribution of (1) X+Y, (2) X-Y, (3) X*Y, (4) X/Y?

(Comment: another very popular quant interview question, regardless of whether the position itself involves statistical modeling)

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5 Responses to Interview Question: Back to Normal

  1. Wu Chao says:

    Hi, Brett, you have more than 1 problem per day.. joking :)(1)&(2) are normal distribution with mean (a+-c) and variance (b+d)

  2. Wu Chao says:

    X*Y may be , need more conditions.However, X/Y is not well defined.

  3. Brett says:

    Wow, Chao, you have to give other readers a chance to figure out by themselves. ūüôā
     
    I try to compile a big list of sample questions to help everyone.¬† If you have any interesting quant questions, please send them my way and I’ll post them here, too.¬† Can’t pay you… but I’ll acknowledge you as the master!¬† ūüôā

  4. qing says:

    Hi, brett, X&Y should be independent, otherwise, this question does not make sense 

  5. Brett says:

    ANSWER
     
    Hi,¬†robertt. Independence is not required to answer this question, but you just pointed out the weakness in¬†superbwu’s answer.¬†¬†If X and Y¬†are not independent of each other, the distribution¬†in each case is some kind of unknown distribution.¬† If X and Y are independent, then in general X+Y and X-Y are also normal, but not X*Y, and as superwu says, X/Y is not even well defined since Y’s distribution includes 0 (even if 0 is in an extreme tail).

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