Week 10

Common continuous RVs; Sum of Normal RVs; and Central Limit Theorem
Published

November 27, 2023

Modified

November 16, 2023

Resources

Chapter Topic Meike’s video Slides Annotated Slides Recording
29 Variance of continuous RVs

31 Uniform RV
32 Exponential RV
33 Gamma RV
35 Normal RV
36 Sums of independent normal RVs
37 Central limit theorem

Exam Materials

  • Practice material

  • Will NOT be cumulative: Chapter 24 - Chapter 35

    • Chapter 31 - 35: Test will use distributions that we learn but will not be asking word problems

      • Think Example 1 from Chapter 32 notes: Tests more on joint pdf than exponential distribution
    • Weeks 7 - 9, with some from Week 10

    • HW 6-7

    • There will NOT be a question using a transformation of X and Y. For example, a question like HW 7, NTB #3 will NOT be on the test.

      • However, a question like 32.10 will be on the test. In that question we are asked about \(P(X<Y)\)
  • During the exam, I will give you scratch paper!

On the Horizon

Announcements 11/27

  • Final Exam on 12/4 (one week from today)

    • Will post materials this afternoon

    • Will NOT be cumulative: Chapter 24 - Chapter 35

  • Be on the lookout for the official course evaluation from SPH

    • Helps me identify the most important areas for improvement

    • Way to directly voice any concerns or appreciation to my supervisors

Announcements 11/29

  • Final Exam on 12/4

  • Again: be on the lookout for the official course evaluation from SPH

    • Helps me identify the most important areas for improvement

    • Way to directly voice any concerns or appreciation to my supervisors

  • Please check that all your homework grades have check marks!

    • There are some missing homeworks!

    • You need to submit all homeworks by end of day 12/8 to get credit!!

Class Exit Tickets

Monday (11/27)

Wednesday (11/29)

Statistician of the Week: Florence Nightingale

Image credit: Henry Hering (1814-1893) - National Portrait Gallery, London

Florence Nightingale

Nightingale was a nurse who is considered to be the founder of modern nursing. In particular, she was admant about the importance of hygiene and sanitary conditions. She was born into a wealthy and well-connected family and had a large amount of privilege. Educated by her father, she showed an ability toward making analytic arguments at an early age. For her work, she was awarded the Royal Red Cross, the Lady of Grace of the Order of St John, and the Order of Merit.

Topics covered

Nightingale was a nurse and statistician who used her analytic abilities to better understand and improve public health. She served in the Crimean War where Britain and France fought against the Russian invasion of the Ottoman Empire. Nightingale worked to convince Queen Victoria that poor sanitation and overcrowding were causing unnecessary death. She was able to show, for example, that peacetime soldiers (who lived in poorly kept barracks) were dying in much higher number than comparable civilian men. Her genius was to collect data meticulously and to display it in ways that were accessible to the general public. Her visualizations are lauded as pioneering and the first of their kind to tell effective stories of important issues.

Relevant work

Image credit: Florence Nightingale, work is in the public domain

“Diagram of the causes of mortality in the army in the East” was published in Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army and sent to Queen Victoria in 1858.

Muddiest Points

1. What were we solving for in the Exponential RV example?

In this example, I was demonstrating how we could make a joint pdf from \(n\) exponential distributions. The joint pdf was for the random variable \(M\) which was the minimum of \(n\) randomly distributed arrival times (\(X_i\)).