Generating random numbers with known mean and variance

Question

From a paper I\'m reading right know:

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S(t+1, k) = S(t, k) + ... + C*∆
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∆ is a standard random variable with mean 0 and variance 1.
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Answer 1

If all you want it a certain mean 0 and variance 1, probably the simplest is this. Do you have a uniform random number generator unif() that gives you numbers between 0 and 1? If you want the number to be very close to a normal distribution, can just add up 12 uniform(0,1) numbers and subtract 6. If you want it to be really exactly a normal distribution, you can use the Box-Muller transform, as Mark suggested, if you don't mind throwing in a log, a sine, and a cosine.