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In some practical applications the alternative, but equivalent, formula for the vari- ance is preferable for computational purposes. That alternative formula is defined by Equation 4.6, which can be verified algebraically (see the chapter appendix). The concept of variance can be very useful in comparing the dispersions of probabil- ity distributions. Consider, for example, viewing as a random variable the daily return over a year on an investment. Two investments may have the same expected returns but will still differ in an important way if the variances of these returns are substantially dif- ferent. A higher variance indicates that returns substantially different from the mean are more likely than if the variance of returns amount is small. In this context, then, variance of the return can be associated with the concept of the risk of an investment-the higher the variance, the greater the risk. Taking the square root of the variance lo obtain the standard deviation yields a quan- lity in the original units of measurement, as noted in Chapter 2. 29 Example 4.4 Expected Value and Variance of Automobile Sales (Expected Value and Variance) In Example 12 Olar Motors, Inc, determined that the number of Prius cars sold daily could vary from 1 to 5, with the probabilities given in Table 4.2 Find the expected value and variance for this probability distribution Links Desktop Local Disk DCS Address