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Normal Distribution

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    x represents values of a Normal random variable X, with parameters [tex]\mu[/tex] and [tex]\sigma^2[/tex]
    z represents corresponding values of normal random variable Z, with parameters 0 and 1.

    z x
    -3 22
    -2 34.5
    1 72
    3 97

    The following questions relate to the tabled data:
    a) calculate the correlation co-efficient between z and x.
    b) calculate the regression equation used to predict x if z is unknown
    c) determine the values of [tex]\mu[/tex] and [tex]\sigma^2[/tex]

    2. The attempt at a solution
    Well the random variable Z has a mean 0 and variance 1, meaning that it is a standard normal distribution.

    a) can I just use a linear regression on the data? this gives a correlation co-efficient of 1
    b) using the same regression, x=12.5z+59.5 ??
    c) Now im stuck.

    Cheers
    Steven
    (sorry I have exams coming up ... hence the rush of posts)
     
    Last edited: Oct 3, 2007
  2. jcsd
  3. Oct 3, 2007 #2

    EnumaElish

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    Science Advisor
    Homework Helper

    "used to predict x if z is unknown" doesn't make sense. You have to know at least one.

    For correlation I wouldn't estimate the regression; just the simple correlation between x and z.

    Independent of 1 and 2, what do you think the answer to 3 might be?
     
  4. Oct 4, 2007 #3
    it cant be as simple as:
    [tex]\mu=0[/tex]
    and
    [tex]\sigma^2=1[/tex]

    can it?
     
  5. Oct 4, 2007 #4
    damn just realised:

    part b should be:
    "calculate the regression used to predict x if z is known"

    sorry
     
  6. Oct 4, 2007 #5
    dont worry finally got it:
    [tex]\mu=59.5[/tex]
    and
    [tex]\sigma=12.5[/tex]

    thanks
     
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