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I hope to calculate $P(X+Y>0 \ |\ Y<0)$, where $X$, $Y$ are independent normal distribution with same mean ($\mu$) and variance ($\sigma$).

I tried to do it with direct integration. That is calculate $P(X+Y>0 \textrm{ and } Y<0)$ first. But failed after I eliminate the first integration sign.

Any other method to calculate this probability?

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    A note on the vocabulary and standard notation: $\sigma$ is called *standard deviation*. When you square $\sigma$, you get what is called the *variance*.2011-09-25
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    Can you show what you tried with integrals? It looks like you might not know LaTeX. To use LaTeX to display the math, type something like \int_a^b\int_c^d f(x,y)\,dy\,dx but surround it with dollar signs. This example is what produces $\int_a^b\int_c^d f(x,y)\,dy\,dx$.2011-09-25
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    Also, if you need to put something with more than one character in the subscript or superscript, surround it with { }. For example, \int_{bottom}^{top}f(x)\,dx makes $\int_{bottom}^{top}f(x)\,dx$2011-09-25

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