Normal Random Variable

1. Mar 24, 2013

twoski

1. The problem statement, all variables and given/known data

X is a normal random variable with mean 1, variance 4.

1. Find P( X(X-1) > 2 )

2. Find a value 'a' for which P(|X| > a ) = .25

3. The attempt at a solution

I had no idea how to start 1.

For 2, i got this far then got stuck:

P(|X| > a) = 1 - P((X-1)/2 <= (a-1)/2) = 1 - Ф((a-1)/2)

2. Mar 24, 2013

LCKurtz

$X^2-X>2$ is the same as $X^2-X-2>0$ or $(X-2)(X+1)>0$. What values of $X$ satisfy that?

$P(X>|a|)=P(X\le -a)+P(X\ge a)$

Is that enough to get you going?

3. Mar 24, 2013

TaliskerBA

For the 1st bit it's the complement of P(-1<X<2) I think.

4. Mar 25, 2013

Ray Vickson

This is incorrect; start over, and be more careful. Draw a picture first, before trying to compute anything!