## Can anyone solve this problem...?

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

Jellis
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 Recognitions: Gold Member Science Advisor Staff Emeritus 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.
 Hi, 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... Jellis