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

You can use the Box-Muller transform.

Suppose U₁ and U₂ are independent random variables that are uniformly distributed in the interval (0, 1]. Let

and

Then Z₀ and Z₁ are independent random variables with a normal distribution of standard deviation 1.