# Can anyone solve this problem ?

• Jellis78
In summary, the conversation is discussing whether a variable that is normally distributed remains normally distributed when raised to the power of 3. It is mentioned that raising the variable to the power of 2 results in a chi-squared distribution. However, it is generally not the case that the cube of a normally distributed variable is also normally distributed. The type of mathematical operation needed to obtain the standard deviation of the transformed variable depends on the specific transformation being applied.

#### Jellis78

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

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,

Of course, If the chi-square distribution is not normal then the cubic isn't 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

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