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**heathrowjohnny** Let $\displaystyle X_1 \sim N(0,2) $ and $\displaystyle X_2 \sim N(0,2) $ be normally distributed random variables that denote a point in $\displaystyle \bold{R}^{2} $. Suppose that the distance squared from this point to the origin is $\displaystyle D^2 = X_{1}^{2} + X_{2}^{2} $. Find the probability that $\displaystyle D > 3 $.

So this is the same as $\displaystyle 1 - P(D^{2} < 9) $. And is $\displaystyle D^{2} $ a $\displaystyle \chi_{2}^{2} $ distribution with $\displaystyle 2 $ degrees of freedom?