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I apologize in advance for misuse of terminology.

If given a number $x$ from a normal distribution with mean 0 and standard deviation 1, how can I map that onto another distribution with a different mean $m$ and standard deviation $s$?

Is it simply $m + s\,x$ ?

Clarification - the real-world problem I'm trying to solve: I would like to generate random numbers in a normal distribution for which I know the mean and standard deviation, however, I can only generate random floating point numbers in a distribution with mean 0.0 and stddev 1.0. How can I translate or "map" this value onto a different distribution?

Gary T.
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  • What exactly do you mean by "mapping"? But I think the answer is "yes". – Peter Flom Nov 02 '13 at 14:11
  • I took the liberty of changing your notation slightly. $n$ suggests first of all sample size in most statistical contexts, presumably not what you intend here. – Nick Cox Nov 02 '13 at 14:14
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    The thread at http://stats.stackexchange.com/questions/5534/transforming-arbitrary-distributions-to-distributions-on-0-1 shows how any continuous distribution (such as a Normal distribution) can be "mapped" (in a meaningful way) to a uniform distribution. Applying the inverse of the mapping for a second distribution gives a transformation between any two continuous distributions. – whuber Nov 02 '13 at 14:14
  • @NickCox. yes, thank you. I don't mean sample size here. – Gary T. Nov 02 '13 at 15:34
  • @PeterFlom I have clarified the question a bit. I hope that helps. – Gary T. Nov 02 '13 at 15:42
  • "I can only generate random floating point numbers in a distribution with mean 0.0 and stddev 1.0": whatever routine you are using should be better documented than that. A mean and standard deviation alone don't define a distribution. At best, such a routine is really producing random normal deviates, but you need to tell us more. – Nick Cox Nov 02 '13 at 15:58
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    The question I linked to in a previous comment answers the revised question. If you're confused by its terminology, then consider researching the probability integral transform. – whuber Nov 02 '13 at 21:32
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    If your question is 'can I take standard normal observations and scale and shift them as indicated to get normal observations with the required mean and standard deviation?' then yes. What are you using that generates standard normals but not general normals? – Glen_b Nov 03 '13 at 03:02

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