# Probability-Central Limit Theorems [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 1 - 1 of 1

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## Question number: 1

» Probability » Central Limit Theorems

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

State and prove Lindeberg-Levy Central limit theorem.

### Explanation

Lindeberg-Levy Central limit theorem.

Let Y 1, Y 2, …, Y n be independent and identically distributed random variables with common mean

E (Y i) =µ and finite positive variance Var (Y i) = σ 2 for i = 1,2, …, n

then , the distribution of the um of these random variables

S n = Y 1 + Y 2 +…+Y n

tends to the normal distribution with mean n µ and varian

… (142 more words) …

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