Reproduce table 5.9 page 207 by using formulas for the 3rd and 5th columns. Reproduce table 5.10 by using formulas for columns for the 2nd, 4th and 6th column.

CHAPTER 5 | 5.1 Introduction to Discrete Probability Distributions 207 TABLE 5.9 | Probability Distribution for Two Statistics Books on Amazon DUMMIES CARTOON GUIDE STARS FREQUENCY PROBABILITY FREQUENCY PROBABILITY 5 42 42/67 = 0.627 113 113/201 = 0.562 4 11 11/67 = 0.164 38 38/201 = 0.189 3 7 7/67 = 0.104 24 24/201 = 0.119 2 3 3/67 = 0.045 16 16/201 = 0.080 1 4 4/67 = 0.060 10 10/201 = 0.050 Total 67 1.00 201 1.00 Using Formula 5.1, we calculate the mean number of stars for each book: Dummies: M = EXP(xi) M = (5) (0.627 ) + (4) (0.164) + (3) (0.104 ) + (2) (0.045 ) + (1) (0.060 ) M = 3.135 + 0.656 + 0.312 + 0.090 + 0.060 M = 4.253 Cartoon Guide: M = Ex;P(xi) M = (5) (0.562) + (4) (0.189 ) + (3) (0.119) + (2) (0.080) + (1) (0.050) M = 2.810 + 0.756 + 0.357 + 0.160 + 0.050 M = 4.133 According to these calculations, the Dummies book has a higher average rating from reviewers than the Cartoon Guide book. Let's next examine the variances and standard deviations. Table 5.10 shows the This column was calculated Table 5.9 variance calculations for both books. TABLE 5.10 | Variance Calculations for Two Statistics Books On Amazon DUMMIES CARTOON GUIDE x 7 P(Xi ) x ? P(x; ) P(x; ) * P(x; ) 5 25 0.627 15.675 0.562 14.050 4 16 0.164 2.624 0.189 3.024 3 9 0.104 0.936 0.119 1.071 2 4 0.045 0.180 0.080 0.320 1 0.060 0.060 0.050 0.050 Total 19.475 18.515 We calculate the standard deviations for the reviews of each book as follows: Dummies: ExFP(x; ) = 19.475 02 = ( EXP(Xi ) ) - 12 02 = 19.475 - (4.253)2 = 19.475 - 18.088 = 1.387 0 = Vo2 = V1.387 = 1.178