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

Do you have any restrictions on the distribution of \Delta ? if not you can just use a uniform distribution in [-sqrt(3), sqrt(3)]. The reason why this would work is because for an uniform distribution [a,b] the variance is 1/(12) (b-a)^2.