# Normal Random Variable

#### twoski

1. Homework Statement

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)

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#### LCKurtz

Homework Helper
Gold Member
1. Homework Statement

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

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

Is that enough to get you going?

#### TaliskerBA

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

#### Ray Vickson

Homework Helper
Dearly Missed
1. Homework Statement

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

"Normal Random Variable"

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