N

where x = a random variable

N = number of trials xi = the outcome of the individual trials.

Mean is also referred as the expectation or average of x and represented by p.

Variance. The variance of x is

£ (Xi - E(x))2 £ (Xi )2 Var (x) = —-n-= ^N-- E(x)2 ...(8.18)

The variance of a process is a measure of how the individual outcomes differ from the mean.

Standard deviation. The standard deviation of a random variable x is given by o(x) = VVar(x) ...(8.19)

The ratio of standard deviation to the mean of a random variable x is given by p(x) = Srr ...(8.20)

8.3.2. Discrete Probability Distributions

While the mean and variance tell a great deal about a random variable, they do not tell us everything. The most complete information is given by the distribution of the random variable. The distribution is the probability associated with each possible outcome.

Mean and variance. The values of P(x1), P(x2), ..., P(xre) for a discrete random process X = x1, x2, ..., x may be plotted as shown in Fig. 8.3.

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