Due: 2020-03-30 by 11:59pm

  1. Assume the population distribution is \(\text{Exponential}(\lambda = 5)\). We’ll use this distribution visualize the Central Limit Theorem. The probability density function for the Exponential distribution is

    \[ f(x | \lambda) = \lambda e^{-\lambda x} \]

    where \(\lambda > 0\) and \(x > 0\).

    1. Plot the density function.

    2. Which direction is the skew of this population distribution?

    3. In a for loop of length R = 501 generate a sample of size N = 1001 from the population. Calculate and store the sample mean of your sample. Don’t forget to pre-allocate your memory.

    4. Make a density plot of the R sample means.

    5. Does the distribution in part a. look like the distribution in part c.? Explain your answer.