Just as any distribution of data, the probability distribution of a random variable X has a mean muX and a standard deviation sigmaX. Just as with a density curve, the mean is the balancing point of the curve. Speaking of the mean, it is determined by the sum of all values x with probabilities p.
The standard deviation sigmaX is just the square root of the variance. The variance being the average squared distance of the values of the variance from the mean. The standard deviation is just the variability of the distribution about the mean.
