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Can anyone solve this problem ?

  1. Nov 3, 2006 #1
    Hi everybody,

    I'm wrestling with the following problem:

    Suppose a variable is normaly distributed, then is this same variable still normal distributed when raised to the power of 3? I know if the variable is raised to the power of 2 a chi-squared distribution is obtained, but what happens when raised to the power of 3?

    I have a feeling that the variable is still normaly distributed but I can't prove it. Let me take this question one bit further; does anyone know what kind of transformation I have to apply to obtain the standard deviation of the transformed varaible?

    Thank you and nice weekend

  2. jcsd
  3. Nov 3, 2006 #2


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    Staff Emeritus
    Science Advisor

    The answer to your first question is, in general no. Any non-linear transformation of a normally distributed variable gives one that is not linearly distributed. I'm not sure why you would accept that the square of a normally distributed variable is not normally distributed but think that the cube would be!
    How you would obtain the standard deviation of a transformed variable depends strongly on the transformation.
  4. Nov 3, 2006 #3

    Thanks for the reply.

    Of course, If the chi-square distribution is not normal then the cubic isnt normaly distributed either.

    I made a excel sheet in which I made the mistake to raise the 3rd power of the frequency instead of the variable of the distribution... No wonder it still looked normally distributed

    I still meant the transformation of raising the 3rd power of a normal distributed variable. So let me rephrase th equestion:

    What kind of mathematical operation do I need to do to obtain the standard deviation of this ‘new’ variable?

    Hope you can link me some sort of solution on the web...:rolleyes:

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