MDM PASCAL'S (6) TRIANGLE (8) 2 3 3 4 6 4 5 10 10 5 (51 6 15 20 15 6 7 21 35 35 21 28 (3) 56 70 56 28 8 G 9 36 04 126 126 84 36 9 G 10 |45 10 (19) (19) 45 120 210 252 210 120 (9) 11. 55 165 330 462 462 330 165 55 11 12 66 220 495 792 924 792 495 220 66 12 (3 (12) 13 78 286 715 1287 1716 1716 1287 715 286 78 13 (2) 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 3) 15 105 455 1365 3003 5095 6435 6435 5005 3003 3 1385 455 105 15 ('S4) 16 560 1820 4368 8008 71 448 12 870 11 448 8008 4368 1820 560 120 161. Given the following function: P11 X = x) = i for the values x = 0, 1, 2, 3, 4, or 5. (a) Show the probability distribution in table form. (b) CaICulate E{X) to 1 decimal place. (:2) Why is this a proper probability distribution? 2. Answer the following about the 1'?\" row (11 = 17) of Pascals Triangle: (a) How many numbers are in the 171h row? (b) What is the sum of the 171:. row? (b) List the first 5 numbers of the 17'\" row ( n = 17} from left to right. Give the numbers not just n_Cr. (C) Using properties of the Pascal's Triangle give an equivalent single combination in the form (n r ) or nCr. (i) (17 4 ) (ii) (17 9 ) + (1'7 10) BONUS (1313}+(1413)+(1513)+{1513)