Law Of Large Numbers, Central Limit Theorem, Normal Distribution, Random Variable, Jacob Bernoulli.
variable with its own mean and variance represented using the notations E(X_bar_n) and Var(X_bar_n) respectively. Suppose that X_bar_n is the mean. Since (X_1, X_2, …, X_n) are i.i.d. variables, it can be shown that: E(X_bar_n) = μ Var(X_bar_n) = σ²/n Now let’s define a new random variable Z_n as