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Possible Duplicate:
Proof of upper-tail inequality for standard normal distribution
Proof that $x \Phi(x) + \Phi'(x) \geq 0$ $\forall x$, where $\Phi$ is the normal CDF

Let $X$ be a normal $N(0,1)$ randon variable. Show that $\mathbb{P}(X>t)\le\frac{1}{\sqrt{2\pi}t}e^{-\frac{t^2}{2}}$, for $t>0$.

Using markov inequality shows that $P(X>t)\le \frac{\mathbb{E}(X)}{t}$ but I dont know how to bound the expected value

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    Suppose that $t>0$ but very close to $0$. Then $P(X>t)$ is very close to $1/2$. But the right-hand side is about $0.4$ when $t$ is very near $0$. The question needs to be modified somewhat.2011-10-22
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    i missed a t at the denominator2011-10-22
  • 2
    In fact, this question has [been added to the faq](http://meta.math.stackexchange.com/questions/1868/list-of-generalizations-of-common-questions).2011-10-22

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