Don't know there are anyone can help me out with this. This is just something I asking myself, not a homework I must say.(adsbygoogle = window.adsbygoogle || []).push({});

Let's define X and Y are 2 standard normal random variables. And random variable Z=X+Y.

For real number a, we know P(X>a), the probability of X is greater than the real number a.

For real number b, we know P(Y>b), the probability of Y is greater than the real number b.

For real number c, we know P(Z>c), the probability of Z is greater than the real number c.

These are simple things.

We also can determine a joint probability P(X>a and Y>b), the probability of X is greater than a, also Y is greater than b. Since X and Y are independent, this joint probability is still simple to know.

What about joint probability P(X>a and Y>b and Z>c)? Because Z is correlated with both X and Y, I don't know how to do this. Thanks for help

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# Joint Probability of Sum Normal

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