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Approximating Gaussian Distribution in Sum of Independent Observations

Learn how the sum of a large number of independent observations from the same distribution approximates a Gaussian distribution, with key properties. Explore Binomial distribution graphs for coin flips.

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Approximating Gaussian Distribution in Sum of Independent Observations

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  1. The sum of a large number of independent observations from the same distribution has an approximate normal (Gaussian) distribution. • Let Wn be the sum of iid (independent identically distributed) • R.V.s): Wn = X1 + X2 + …. + Xn • Wn has approximate Gaussian distribution with: • E[Wn]=nE[X] • Var[Wn]=nVar[X]

  2. Flip coin n times, Binomial (n,1/2), graphs for n=5,10, 20

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