*Simillar Question

State central limit theorem with its importance

The Central Limit Theorem (Liapounoff’s Form)

    If $X_1,X_2,X_3…..X_n…..$ be a sequence of independent identically distributed RVs with $E(X_i )=μ_i$ and $Var(X_i )=σ_i^2, i=1,2….$ and if $S_n=X_1+X_2+⋯.X_n$ then under certain general conditions, $S_n$ follows a normal distribution with mean $μ=∑_{i=1}^n μ_i$ and variance $σ^2=∑_{i=1}^n σ_i^2$ as n tends to infinity.

Central …