- The probability distribution of a random variable , like a distribution of data, has a
**mean**and a**standard deviation**. - The
**law of large numbers**says that the average of the values of observed in many trials must approach . - The
**mean**is the balance point of the probability histogram or density curve. If is**discrete**with possible values having probabilities , the mean is the average of the values of , each weighted by its probability:236

- The
**variance**is the average squared deviation of the values of the variable from their mean. For a discrete random variable, - The
**standard deviation**is the square root of the variance. The standard deviation measures the variability of the distribution about the mean. It is easiest to interpret for Normal distributions. - The
**mean and variance of a continuous random variable**can be computed from the density curve, but to do so requires more advanced mathematics. The means and variances of random variables obey the following rules. If and are fixed numbers, then

If and are any two random variables having correlation , then

If and are

**independent,**then . In this case,