If two random variables X and Y are connected by relation \frac{2X-3Y}{5X+4Y}=4 and X follows Binomial distribution with parameters n=10 and p=\frac{1}{2}, then what is the variance of Y?

Explanation

Simplify the given relation: 2X - 3Y = 20X + 16Y \implies 19Y = -18X \implies Y = -\frac{18}{19}X. The variance of Y is Var(Y) = (-\frac{18}{19})^2 Var(X) = \frac{324}{361} Var(X). For the Binomial distribution of X, Var(X) = npq = 10(\frac{1}{2})(\frac{1}{2}) = \frac{5}{2}. Therefore, Var(Y) = \frac{324}{361} \times \frac{5}{2} = \frac{810}{361}.

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