Return to Question

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

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

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

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

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

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