Is 2 times normal distribution still a normal distribution please?

In summary, The question asked is whether the equation 3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) represents a normal distribution with mean 0 and variance delta^2. The conversation also mentions the relation to kurtosis and the possibility of fitting a normalized PDF with the form A exp(-x^2/B) to obtain a normal distribution. The answer is that for any positive values of A and B, the normalized equation A exp(-x^2/B) will result in a normal distribution.
  • #1
wall_e
4
0
Hi, it will be a very silly question, excuse me please.

I am wondering whether

3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) is still a normal distribution please?


where mean is 0, delta^2 is the variance.


Thank you very very much.

Also, how to understand this related to the kurtois please? Many many thanks again.
 
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  • #2
It is not a normalized PDF, since the total probability sums up to more than 1.
 
  • #3
thank you very much, pmsrw3.

So if I want to choose a form A exp(-x^2/B) to fit a pdf, where A and B are parameters, after normalization, I will get a normal distribution?
 
  • #4
Yup, for any A,B > 0, A exp(-x^2/B), normalized, is a normal distribution.
 
  • #5
Oh, thank you very much! pmsrw3
 

FAQ: Is 2 times normal distribution still a normal distribution please?

What is a normal distribution?

A normal distribution is a type of probability distribution that follows a bell-shaped curve, with most values clustering around the mean and decreasing as they move further away from the mean. It is also known as a Gaussian distribution.

What does it mean for a distribution to be "normal"?

A "normal" distribution means that the data follows the characteristics of a normal distribution, such as the bell-shaped curve and the mean and standard deviation determining the shape and spread of the distribution.

How is a normal distribution defined mathematically?

A normal distribution is defined by two parameters: the mean (μ) and the standard deviation (σ). The equation for a normal distribution is f(x) = e^(-(x-μ)^2/2σ^2)/(σ√(2π)), where e is the base of the natural logarithm, x is the variable, μ is the mean, and σ is the standard deviation.

Can a distribution with a mean of 0 and a standard deviation of 2 still be considered a normal distribution?

Yes, a distribution with a mean of 0 and a standard deviation of 2 can still be considered a normal distribution. The mean and standard deviation determine the shape and spread of the distribution, and a normal distribution can have any combination of values for these parameters.

Is 2 times normal distribution still a normal distribution?

Yes, multiplying a normal distribution by a constant (in this case, 2) will still result in a normal distribution. The shape of the distribution will remain the same, but the values on the x-axis will be multiplied by the constant. This will affect the mean and standard deviation of the distribution, but it will still follow the characteristics of a normal distribution.

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