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Homework Help: What is the inverse of h(y) where y=|x|

  1. Feb 26, 2006 #1
    I'm preparing for my Statistics and Probability exam tomorrow, and I have a quick question:

    What is the inverse of h(y) where y=|x|. (just to make sure, h'(x)=1, right?)
     
  2. jcsd
  3. Feb 26, 2006 #2

    0rthodontist

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    h'(x) is not 1 for all x. Draw the graph of |x| and think again. Also do you know the horizontal line test for whether a function is invertible?
     
  4. Feb 26, 2006 #3
    Well when I draw the graph for |x| i get like a graph like this starting at the origin \|/ , and I'm not sure how to find the inverse or by using the horizontal line test? is that like one-to-one function type?
     
  5. Feb 26, 2006 #4
    This is the problem that I'm doing:
    Suppose that Z is a standard normal random variable: i.e. Z~N(0,1).
    a) Find the distribution of X=|Z| .
    b) What is the density of X?
    c) Find the distribution of Y=X^2
    d) What is the joint distribution of X and Y?
    ------------------------------------------
    For a) P(X</=x) = P(|Z|</= x) = P(-z</= x </= z) = P(x</=z) - P(x</= -z)
    I'm stuck here...

    For b) is the density function for this the same as the one that is given as the definition. I mean fx(x)=[1/root2(pie)]e^(-x^2)/2?

    For c) I got N(0, 2root(y)) as the distribution of Y=X^2.
     
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