6. Suppose that ( X_{1}, ldots, X_{n} ) are independent, with ( X_{i} ) being normal with mean ( mu_{i} ) and variance ( sigma_{i}^{2}, i=1, ldots, n ). Let ( S_{n}=sum_{i=1}^{n} X_{i} ). a. What is the conditional distribution of ( X_{n} ) given that ( S_{n}=x ) ? b. Explain how you could generate ( X_{1}, ldots, X_{n} ) conditional on ( S_{n}=x ).
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