Assume you have \(N\) random variables \(X_1, \ldots, X_N \sim_{iid} \text{Normal}(\mu, \sigma^2)\).

  1. True or false: is, or at least should we, think about \(\frac{1}{N}\sum_{n = 1}^N X_n\) as a random variable?

  2. Assume you have bootstraped your original dataset above, to get re-sampled estimates of the population mean, and you now have an array of bootstrapped sample means mus of length \(R\).

    1. What does the Python code mus.std() estimate? For full credit use our latest statistics words.

    2. What does the Python code bp.density(mus) estimate? For full credit use our latest statistics words.