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I think everyone knows that

Q(x)= P(X>x) where X is a Gaussian Random variable.

Now I was reading about it and it says that Q(x) is bounded as follows

Q(x)≤ (1/2)(e

and

Q(x)< [1/(√(2∏)x)](e

and the lower bound is

Q(x)> [1/(√(2∏)x)](1-1/x

Can you tell me how you get this?

Thanks a lot.

Q(x)= P(X>x) where X is a Gaussian Random variable.

Now I was reading about it and it says that Q(x) is bounded as follows

Q(x)≤ (1/2)(e

^{-x2/2}) for x≥0and

Q(x)< [1/(√(2∏)x)](e

^{-x2/2}) for x≥0and the lower bound is

Q(x)> [1/(√(2∏)x)](1-1/x

^{2}) e^{-x2/2}for x≥0Can you tell me how you get this?

Thanks a lot.

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