Stochastic exponential growth can be simulated by adding a random variable sZ to the value of R, so that

where s, the standard deviation, measures the amount of random variability we wish to include, and Z is a standard normal deviate, a value selected at random from a standard normal distribution with mean and standard deviation s = 1.

The normal (or Gaussian) distribution is the familiar unimodal, symmetric curve with thin tails that every introductory textbook calls the "bell curve." Here is a picture (courtesy A.A. Sharov) of a normal distribution showing the important facts about the normal curve.

Confidence interval (c.i.) is the interval where the sample mean can be found with probability of (1- P), where P is error probability (e.g., P=0.05). The number of degrees of freedom d.f. = N-1 (one d.f. goes for estimation of sample mean). One standard deviation around the mean contains 66% of the area of the normal curve while 1.96 standard deviations contains 95% of the area of the curve. Hence, the 95% confidence interval is represented by the region 1.96 standard deviations to either side of the mean.

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