Saved Bookmarks
| 1. |
23. Two numbers are selected at random (withoutreplacement) from the first five positive integers. LetX denote the larger of the two numbers obtained.Find the mean and variance of X |
|
Answer» Let X denote the larger of two numbers The two positive integers can be selected from the first six positive integers without replacement in 5x4 = 20 ways X represents the larger of the two numbers obtained. Therefore, X can take the value of 2, 3, 4, 5 For X = 2, the possible observations are (1, 2) and (2, 1).P(X=2) = 2/20 For X = 3, the possible observations are (1, 3), (2, 3), (3, 1), and (3, 2).P(X=3) = 4/20 For X = 4, the possible observations are (1, 4), (2, 4), (3, 4), (4, 3), (4, 2), and (4, 1).P(X=4) = 6/20 For X = 5, the possible observations are (1, 5), (2, 5), (3, 5), (4, 5), (5, 4), (5, 3), (5, 2), and (5, 1).P(X=5) = 8/20 Mean[E(X)] = 2*2/20 + 3*4/20 + 4*6/20 + 5*8/20= 4/20 + 12/20 + 24/20 + 40/20= 80/20 = 4 E(X^2) = 2^2 *2/20 + 3^2*4/20 + 4^2*6/20 + 5^2*8/20= 8/20 + 36/20 + 96/20 + 200/20= 340/20 = 17 Variance = E(X^2) - [E(X)]^2= 17 - 16= 1 your answer is wrong mean come 4 and var... come 1 |
|