Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose you have two random variables $X$ and $Y$. If $X \sim N(0,1)$, $Y \sim N(0,1)$ and you want to find k s.t. $\mathbb P(X+Y >k)=0.01$, how would you do this? I am having a hard time finding the limits of integration. How would you generalize $\mathbb P(X+Y+Z+\cdots > k) =0.01$? I always get confused when problems involve multiple integrals.

share|cite|improve this question
up vote 4 down vote accepted

Hint: Are the random variables independent?

If so, you can avoid integration by using the facts

  • the sum of independent normally distributed random variables has a normal distribution

  • the mean of the sum of random variables is equal to the sum of the means

  • the variance of the sum of independent random variables is the sum of the variances

  • for a standard normal distribution $N(0,1)$: $\Phi^{-1}(0.99)\approx 2.326$

share|cite|improve this answer
And if they are not independent, then knowing the distribution of each of them is not enough anyway. – Henning Makholm Nov 13 '11 at 5:37

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.