Question: Let X, Y be independent random variables \(X\tilde{\ }Bi\left( {{m}_{1}},{{\pi }_{1}} \right)\), \(Y\tilde{\ }Bi\left( {{m}_{2}},{{\pi }_{2}} \right)\).

a) Normalize \(\frac{X}{{{m}_{1}}}-\frac{Y}{{{m}_{2}}}\)

b) Let x = 264, y = 496. Compute the realization of the normalized random variable \(\frac{X}{{{m}_{1}}}-\frac{Y}{{{m}_{2}}}\).You know that \(X\tilde{\ }Bi\left( 300,0.85 \right)\) and \(Y\tilde{\ }Bi\left( 620,0.83 \right)\).