Game 11: Simulation-I

Central Limit Theorem

Let X_1, \cdots, X_n \sim with common mean and variance E(X_i) = \mu, Var(X_i) = \sigma^2 for all i. Then for all t

P( \frac{\bar{X}-\mu}{\sigma \sqrt{n}} \leq t ) \rightarrow \Phi(t)

as $n \righarrow \infty$

where \bar{X} = \frac{1}{n} \sum_{i=1}^n X_i and \Phi(t)=P(Z \leq t) and Z \sim N(0,1).

R Notebook for Game 11

 

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s