Stacking Gaussians

Let X,Y,Z X, Y, Z be independent random variables, each distributed as N(12,12) N(12, 12) (mean 1212, variance 1212). The probability P[X−Y>Z] P[X - Y > Z] can be written as Φ(a) \Phi(a) , where Φ \Phi is the standard normal CDF. Find a a .

Answer

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