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

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

Wow, Chao, you have to give other readers a chance to figure out by themselves. 🙂

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! 🙂

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

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).