(a) Bar chart (b) Histogram

Fig. 8.3. Discrete probability distribution.

The value of x corresponding to the centre of gravity of the above diagram is called the average or mean or expectation E(x)

P(xp must be non-negative and must sum to 1. The mean || is also known as the first moment of the random variable. |ik , the kth moment of the random variable is defined as

The variance Var(X) or o2 is a measure of the dispersion or spread of the histogram. It is defined as the mean squared deviation of x from the mean.

The variance is generally referred as second centrol moment. The kth central moment is defined as

The standard deviation, o if defined as the square root of the variance.

x x x x n dice) is P1 = P2 = P3 = P4 = P5 = P6 = — . Find the mean, variance and standard deviation.

Example 8.4. The distribution for the outcomes of rolling a single die (half a pair of

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