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In the past, drawing a .Q: Generate a random number within a certain range I have a Vector of length N. I want to generate a random number in range [0,l]. A: This is what distribution functions are for: you find a probability distribution that describes your random variable, such as a normal distribution, and plug in the relevant parameter values. The normal distribution is defined by $$ \text{normal(}\mu,\, \sigma^2 \text{)} \triangleq \frac{1}{\sqrt{2\pi \sigma^2}} e^{ -\frac{(x – \mu)^2}{2 \sigma^2}}$$ or $$ \mathbb{P}(N \leqslant \text{normal}(0,\, \sigma^2)\, l \leqslant N) \triangleq \mathbb{P}(\frac{\text{normal}(0,\, \sigma^2)\, l – \mu}{\sigma} \leqslant \frac{N – \mu}{\sigma} \leqslant \frac{\text{normal}(0,\, \sigma^2)\, l – \mu}{\sigma})$$ A: Usually it’s easier to define a cumulative distribution function, then either the upper or lower quantile. In the case of a uniformly random number between 0 and l, and in the limit that l is very large compared to n, the quantile function is $$ x = \frac{l+n-1}{2n} + \frac{1}{2n}\sqrt{\frac{(l-n)^2}{4n^2} + 1}, $$ which is the upper quartile for a standard normal random variable. For very small values of l, we instead have $$ x = \frac{l+n-1}{2n} – \frac{1}{2n}\sqrt{\frac{(l-n)^2}{4n^2} + 1}. $$ Depending on your needs, you can then subtract the appropriate number from this to get a number in your desired range. Format: c6a93da74d
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