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Normal Random Variable

  1. Mar 24, 2013 #1
    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. jcsd
  3. Mar 24, 2013 #2

    LCKurtz

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    ##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?
     
  4. Mar 24, 2013 #3
    For the 1st bit it's the complement of P(-1<X<2) I think.
     
  5. Mar 25, 2013 #4

    Ray Vickson

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