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Math Help - S^2 is variance of sample from normal distribution - what is distribution of cS^2?

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    S^2 is variance of sample from normal distribution - what is distribution of cS^2?

    If S^2 is the variance of a random sample which is drawn from a normal distribution N(\mu,\sigma^2) then cS^2 has a standard distribution for a particular value of the constant c.

    Specify the constant c. What is the distribution?

    How many pairs of positive constants a; b exist such that P(a < cS^2 < b) = 0.95?
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    Quote Originally Posted by Amanda1990 View Post
    If S^2 is the variance of a random sample which is drawn from a normal distribution N(\mu,\sigma^2) then cS^2 has a standard distribution for a particular value of the constant c.

    Specify the constant c. What is the distribution?

    How many pairs of positive constants a; b exist such that P(a < cS^2 < b) = 0.95?
    You're expected to know (or find out eg. Variance - Wikipedia, the free encyclopedia) that \frac{(n-1) S^2}{\sigma^2} ~ \chi^2_{n-1}.

    Use this to answer the second part of your question.
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    I see! Thing is, surely the answer to the second part of the question is "infinitely many"? Do you think we're supposed to identify all the possible intervals [a,b]?
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    Quote Originally Posted by Amanda1990 View Post
    I see! Thing is, surely the answer to the second part of the question is "infinitely many"? Do you think we're supposed to identify all the possible intervals [a,b]?
    Answer the question as asked (explain why that is the answer).

    .
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