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 ...

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

Question:

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 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.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...