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Math Help - random variable

  1. #1
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    random variable

    the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

    Calculate P(V \geq 1)

    confused!
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by skystar View Post
    the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

    Calculate P(V \geq 1)

    confused!
    P(V \ge 1)=P(U^2 \ge 1)=P(|U| \ge 1)=P(U<-1)+P(U>1)

    Does this help ?
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  3. #3
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    hmmm not really
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    Moo
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    Quote Originally Posted by skystar View Post
    hmmm not really
    Then, you use the normal distribution, by transforming it into a standard normal distribution (Normal distribution - Wikipedia, the free encyclopedia). Everything is in the link...
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  5. #5
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    arh i see how did you know to go from  U^{2} to |U|?
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  6. #6
    Moo
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    Quote Originally Posted by skystar View Post
    arh i see how did you know to go from  U^{2} to |U|?
    I took the square root

    a=b^2 \implies b=\pm \sqrt{a} \Longleftrightarrow |b|=\sqrt{a}

    This is quite the same here ^^


    Edit : I'm sorry, I misread the question... Well, we know the law for U, not for UČ. And from one to another, there is only the step mentioned above
    Last edited by Moo; June 1st 2008 at 01:03 PM.
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  7. #7
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    Quote Originally Posted by skystar View Post
    the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

    Calculate P(V \geq 1)

    confused!
    The more interesting question is to find the pdf for V (you'll find it done a couple of times in different contexts on these boards). Then you can check the answer you got using Moo's excellent help .
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