Solving Normal Random Variable Equations for P(X(X-1) > 2) and P(|X| > a)

[twoski]

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

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)

 

[LCKurtz]

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

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 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

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!