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Sam is writing a research paper for his graduation. On his draft of the paper, there...

Sam is writing a research paper for his graduation. On his draft of the paper, there are an average of 5 typos on each page. Assume each typo is independent.

a) Let Y to be the number of typos in Chapter 1, which is 4 full pages in length. What is the probability that there are 18 typos in the first chapter? What is the distribution, parameter(s), and support of Y?

b) What is the probability that Sam has 18 to 20 typos (inclusive) in the draft of Chapter 1?

c) What is the expected value and variance of Y?

d) What is the probability that Sam has 10 typos in Chapter 1 and 10 typos in Chapter 8 (which is 5 pages)?

e) It turns out that the first 4 chapters have the same number of pages (4 pages), what is the probability that Sam has 18 to 20 typos (inclusive) in 2 of the 4 chapters of his draft?

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