What maximum and minimum number this MATLAB function normrnd(mu,sigma) can output? If the mean = 0 and S.D =2? and what happen if we increase the S.D in this fucntion.
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Luis Mendo
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So the sigma in this function is σ. If I say my sigma=2 and mean = 0 than it means that there will be 95% random numbers that will be generated within -4 and 4? and 68% of the random number generated will be between -2 and 2? – Geek Jun 18 '14 at 18:13
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That's correct, but of course only in an approximate sense. The generated numbers are random after all – Luis Mendo Jun 18 '14 at 22:04
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Ideally, there are no such maximum and minimum. A normal (Gaussian) pdf has infinite support, so it can produce any value, no matter how high or low, with positive probability. Of course, exceeding a value x is less probable as x grows; but the probability is never 0.
In reality, Matlab cannot represent values with absolute value greater than realmax (about 10^308). But that's a very large number, and the probability of reaching a value close to that is very small.
The S.D is a scale factor of the distribution. A greater S.D. tends to produce random numbers with larger absolute value. You can think about it this way: you generate a number according to a standard_ normal distribution (0 mean, 1 S.D.), and then you multiply times the actual S.D. and add the actual mean.
Luis Mendo
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