# Question: The following is a sufficient condition the Laplace Liapounoff condition for

The following is a sufficient condition, the Laplace-Liapounoff condition, for the central limit theorem: If X1, X2, X3, . . . is a sequence of independent random variables, each having an absolute third moment

And if

Where Yn = X1 + X2 + · · · + Xn, then the distribution of the standardized mean of the Xi approaches the standard normal distribution when n → ∞. Use this condition to show that the central limit theorem holds for the sequence of random variables of Exercise 8.7.

And if

Where Yn = X1 + X2 + · · · + Xn, then the distribution of the standardized mean of the Xi approaches the standard normal distribution when n → ∞. Use this condition to show that the central limit theorem holds for the sequence of random variables of Exercise 8.7.

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