One invests 100 shares of IBM stocks today. He expects that there could be five possible opening prices with the respective probabilities at 9:30 a. m. in NYSE the next day. The following table lists these possible opening prices and their respective probabilities: Outcome 1 Outcome 2 Outcome 3 Outcome 4 Outcome 5
Possible Opening
Price of IBM, Xi $182.11 $163.88 $180.30 $216.08 $144.92
Probability, pi 13% 19% 33% 17% 18%
Let X represent the five random opening prices of IBM the next day, calculate the mean, variance, and the standard deviation of X. Make your comments on the results you obtain.