Due: 2019-10-22 by 11:59pm

https://classroom.github.com/a/MjcxNNm3

  1. Assume the population is Normal, with \(\mu\) a real number and \(\sigma > 0\) of your choice.

    1. Pre-allocate an array of size \(R\).

    2. Generate \(N\) Normal random variables. Use the function \(\texttt{numpy.random.normal}(\mu, \sigma, N)\). Name this array X.

    3. In a for loop of length \(R\),

      • create an array of randomly chosen integers from \(0\) to \(N - 1\), with replacement. Name this array idx.
      • use Scipy’s function minimize to estimate just the population mean, using the array of random variables just generated. Instead of passing in X, pass in X indexed with idx, as your data. Store the estimate into the \(r\)th element of your pre-allocated array.
    4. Estimate the population standard deviation of the sample mean using the array of sample means.

    5. What is the name of this quantity?

    6. Explain, in complete English sentences, what the standard deviation of the sample mean is telling us.

    7. Make a plot density plot using the array of sample means.

    8. What is the name of this density function?

    9. Repeat steps a. through h. using the other sample size, overlaying the two density plots on each other. Use the color and label arguments of bp.density() to differentiate the two density curves on the same plot. Call bp.legend() after your done plotting.

    10. Explain, in complete English sentences, why your two density curves look different.