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Math Help - Chi squared distribution

  1. #1
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    Chi squared distribution

    Can someone please help me with the attached problem, I really don't know where to start with it. I'd really appreciate some pointers in the right direction.

    Thanks.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    note that  Y = \frac{1}{\sigma^2} (X_i-\mu)^2 has a chi-squared distribution of  n degrees of freedom since each term in the sum is a squared normal random variable and is independent of other random variables in the sum. Then show that  Y - \frac{(n-1)S^2}{\sigma^2} = \left(\frac{\bar{X} - \mu}{\sigma/ \sqrt{n}} \right)^2 . The RHS is a chi-squared random variable with one degree of freedom. Since df's add, this implies that  \frac{(n-1)S^2}{\sigma^2} is a chi-squared distribution with  n-1 degrees of freedom provided that  \frac{(n-1)S^2}{\sigma^2} and  \left(\frac{\bar{X} - \mu}{\sigma/ \sqrt{n}} \right)^2 are independent.
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  3. #3
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    Thanks, just one question


    where does the Y= value come from?/ What does it represent in? (sorry for being so slow at this question)

    Thanks for your help.
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