Q: Let the random variables X and Y have joint density function given by f_{X,Y}(x,y) = { C(1 − y), 0 ≤ x ≤ y ≤ 1 { 0, otherwise Then the marginal density function for X is
(a)f_X(x) = 6(½ x − x²/2) for 0 ≤ x ≤ 1
(b)f_X(x) = 6(½ x + x²/2) for 0 ≤ x ≤ 1
(c)f_X(x) = 6(½ + x − x²/2) for 0 ≤ x ≤ 1
(d)f_X(x) = 6(½ − x + x²/2) for 0 ≤ x ≤ 1
Correct Answer: (d)
The correct answer is (d): f_X(x) = 6(½ − x + x²/2) for 0 ≤ x ≤ 1. Subject: Geography | Sub-topic: Population & Demography Note: This answer was determined through AI-based research. Verify against the official answer key when available.