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.
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Hint: Are the random variables independent?
If so, you can avoid integration by using the facts