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A probability density fucntion is given by $p(x)=\mathrm{K} e^{-x^2 / 2}-\infty<x<\infty$. The value of $K$ should be

  1. $\frac{1}{\sqrt{2 \pi}}$
  2. $\sqrt{\frac{2}{\pi}}$
  3. $\frac{1}{2 \sqrt{\pi}}$
  4. $\frac{1}{\pi \sqrt{2}}$
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