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Math Help - chi squared

  1. #1
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    chi squared

    Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
    Determine a value of c such that the random variable cY will have a chisquared distribution

    Any clues on this?? Thanks!
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  2. #2
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    Quote Originally Posted by holly123 View Post
    Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
    Determine a value of c such that the random variable cY will have a chisquared distribution

    Any clues on this?? Thanks!
    The first thing I'd do is get the (well known) distributions of U1 = X1 + X2 + X3 and U2 = X4 + X5 + X6.

    Then I'd think about the distributions of V1 = U1^2 and V2 = U2^2, and I'd also be thinking about the well known distribution of X^2 .....

    Then I'd be thinking about the distribution of W = V1 + V2, in light of the above.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by holly123 View Post
    Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
    Determine a value of c such that the random variable cY will have a chisquared distribution

    Any clues on this?? Thanks!
    The sum of the squares of k standard normal RV's has a chi-squared distribution with k degrees of freedom.

    CB
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