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STA 462R Project 1
Name:_________________
Q1. (20pts) As part of Chapter 6 we learned that not all distributions have a moment generating functions.
One of them is the Cauchy distribution. See https://en.wikipedia.org/wiki/Cauchy_distribution
a)(5pts) Explain using mathematical notations/formulas, why it is not possible to derive MGF for this
distribution. Why is this distribution refer to as a “pathological” distribution?
b)(5pts) Crate a plot of Cauchy PDF for 4 different distribution with 𝑥0 = −2 and
𝛾 = 0.5; 1; 2; 3. All of these PDFs should be plotted on the same plot. Format your plot
properly, add legend inside the plot, use different colors for the density lines, etc.
c)(5pts) Create a plot of Cauchy CDFs for the same parameters given in part b) above.
d)(5pts) Reflect on this question. Elaborate on your observations and findings. Write at least 5 full
sentences in order to earn full credit. Think about the following questions as you write your reflection:
What do I observe from the plots? Does this question improve my understanding of Chapter 6 material?
What did I learn going through this exercise? Who cares about Cauchy distribution?
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