If two random variables X and Y are connected by relation (2X - 3Y)/(5X + 4Y) = 4 and X follows Binomial distribution with parameters n = 10 and p = 1/2, then what is the variance of Y?
A.810/361✓ Correct
B.9/19
C.21/361
D.121/361
Explanation
From (2X - 3Y)/(5X + 4Y) = 4: 2X - 3Y = 20X + 16Y, so -18X = 19Y, giving Y = -18X/19. Variance of X for binomial = npq = 10·(1/2)·(1/2) = 5/2. Var(Y) = (18/19)² · Var(X) = (324/361) · (5/2) = 1620/722 = 810/361.
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