# 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

Appeared in Year: 2013

### 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

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