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(a) Let the sequence of n random variables {X1,X2,,Xn}, independently obtained from some
probability density function pX(x). If E[Xi]= and Var(Xi)=2 are finite then, as n increases to
infinity, according to the Central Limit Theorem the random variable S=4n(Xn) approaches
which distribution? Justify its type (name), and hence compute its mean and variance.

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(a) Let the sequence of n random variables {X1,X2,�,Xn}, independentl.pdf

  • 1. (a) Let the sequence of n random variables {X1,X2,,Xn}, independently obtained from some probability density function pX(x). If E[Xi]= and Var(Xi)=2 are finite then, as n increases to infinity, according to the Central Limit Theorem the random variable S=4n(Xn) approaches which distribution? Justify its type (name), and hence compute its mean and variance.