.. title: Engineering Probability Homework 1 due Thurs 2019-01-17 .. slug: homework01 .. date: 2019-01-10 .. tags: mathjax .. category: homework .. link: .. description: .. type: text How to submit ------------- Submit to LMS; see details in syllabus. Questions --------- #. (6 pts) One of the hardest problems is forming an appropriate probability model. E.g., suppose you're working for Verizon deciding how much data capacity your network will need once it starts selling the iphone. Suppose that you know that each customer will use 5GB/month. Since a month has about 2.5M seconds, does that mean that your network will need to provide only 2KB/s per customer? What might be wrong with this model? How might you make it better? (This is an open-ended question; any reasonable answer that shows creativity gets full points.) #. (3 pts) One hard problem with statistics is how they should be interpreted. For example, mental health care professionals observe that young men with schizophrenia usually smoke pot (marijuana). Assuming for the sake of argument that this correlation is real, does this mean that pot smoking causes schizophrenia? *Historical note:* In 1974, the question of whether cigarette smoking causes lung cancer was answered by forcing some dogs in a lab to smoke and observing that they got cancer more than otherwise identical dogs not forced to smoke. The tobacco companies were maintaining that the strong correlation between smoking and lung cancer (1/4 of smokers died from cancer) did not demonstrate a causal relation. Maybe there was a common cause for both a desire to smoke and a likelihood to later get cancer. These experiments refuted that claim. `Mary Beith, the journalist who broke the 'smoking beagles' story `_ #. (6 pts) Do exercise 1.3 in the text on page 19. #. (6 pts) Do exercise 1.6 on page 19. #. (6 pts) Do exercise 1.11 on page 20. Total: 27 pts.