Nora's observation is correct about X being standard normal or just arbitrarily normal.

But since we can always transform any arbitrary normal to standard normal I think focusing on the latter case is sufficient.

The solution is not hard: Let X be N(0,1), and let Y be |X|. Just use the cumulative distribution function:

P(Y

Well I could sit here and theorize about this and work on some derivation. But it would seem that it's easier to generate/simulate data based on your parameters (mean and std), followed by the applying the function in which you are interested. Then I would plot the observations. It's rather crude. BUT, the absolute of a normally distributed data will be very different with mean of 0 and std of 1 vs a mean of 10 and std of 1.

Nora's observation is correct about X being standard normal or just arbitrarily normal.

But since we can always transform any arbitrary normal to standard normal I think focusing on the latter case is sufficient.

The solution is not hard: Let X be N(0,1), and let Y be |X|. Just use the cumulative distribution function:

P(Y

Well. If the random variable has a mean equal to zero, then the absolute value of it will have a semi- normal distribution. If the mean is mu0 then the distribution of the absolute value of (x-mu) will have a semi-normal distribution...Otherwise , I think it will not have a known distribution.

I attach my answer, I suppose it is correct. I think that in the answer of Tsung Fei Khang there is a typing error P(-y

There is a typo in the FOURTH line of Andrea Martinelli's attachment. Phi((-mu-y)/sigma)-Phi(-(mu+y)/sigma) should be Phi((-mu+y)/sigma)-Phi(-(mu+y)/sigma).

Similar typos appeared in the third to last and last lines.

Thanks, it is the copy and paste. I hope that I have corrected all the typos.

The distribution of the absolute of a normal distribution is called a folded normal distribution, see e.g. Johnson, Kotz and Balakrishnan.

I think that the attached gives the answer to the first part (but it is very easy to make mistakes with this sort of thing). Stephen

Dear Raja. The distribution of the absolute value of a random variable with normal distribution is called folded normal distribution. Check the link to use the folded normal simulator. Hope it helps. Cheers.

http://www.math.uah.edu/stat/applets/SpecialSimulation.html

For zero mean:

http://en.wikipedia.org/wiki/Half-normal_distribution

http://mathworld.wolfram.com/Half-NormalDistribution.html

In the open source statistics software R, www.r-project.org, you might want to consider contributed package "distr", cran.r-project.org/web/packages/distr , which provides arithmetics acting on distributions/random variables. So you get answers to your questions by the following code:

#------------------------------------------------

require(distr)

#------------------------------------------------

X

Nora Ruel iam intrsted only in standard normal

Thanx alot to all of you for your response, that was really helpful , ma god bless you with more and more success

The distribution of absolute normal random variable is Folded Normal Distribution.

See the following reference; http://www.tandfonline.com/doi/abs/10.1080/00401706.1961.10489974#.Ue-wbEphBC8

Also to find maximum of two folded normal random variable you can use the order statistics formulation.

Dear Raja, have you managed to find the distribution of the max ?