1 _ n (£ J + n(n - 1) G £ J _ n(n - 1)(n - 2) G £
where £ = mean and equation 8.31 is a poisson distribution. Variance o2 = £ (also). 8.3.3. Continuous Probability Distributions
The random process may be discrete or continuous. For continuous function, the histogram (Fig. 8.3(b)) becomes a continuous. As probability P(x) tends to zero, the probability density function p(x) is plotted against x. The probability density p(x) is defined by and fb p(x) = P(a < x < b) = I p(x) dx Ja
J p(x) dx = 1 For continuous distribution,
Variance, o2 = J x2 p(x) - £2 For independent random variable X and Y, mean, E(X ± Y) = E(X) + E(Y) ...(8.35)
Negative exponential distribution. The probability that the interval between event T, will exceed time t is given by p (T > t) = e
where T is the mean interval between events.
Gaussian or normal distribution. A random variable, x is said to be normally distributed if its density function has the form
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