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Normal Random Variable

  • Thread starter twoski
  • Start date
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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)
 

LCKurtz

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

Ray Vickson

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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!
 

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