The following is a sufficient condition, the Laplace Liapounoff condition, for the central limit theorem If X 1 , X 2 , X 3 , is a sequence of independent random variables, each having an absolute third moment And if Where Y n X 1 X 2 X n , then the distribution of the standardized mean of the X i 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 m Yar

Question: The following is a sufficient condition, the Laplace-Liapounoff condition, for the central limit theorem: If X 1 , X 2 , X 3 , .

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

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And if

Where Y_n = X₁ + X₂ + · · · + X_n, then the distribution of the standardized mean of the X_i 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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