STA 395 HW 1

Questions 1-6 are from the textbook. You are allowed to use R for any of these, but please plan on turning a hard copy of your solutions into class (handwritten or printed is OK)

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Question 1: 1.3

Question 2: 1.4

Question 3: 1.7. For Part (b), compare the probability distribution given with a binomial. Identify why the distribution function given should be used instead of the binomial

Question 4: 1.12. Part (d) is optional. However, see if you can’t find a way to confirm these values using only functions in base R (i.e., without installing and using an external package).

Question 5: 1.13

Question 6: 1.15

Question 7:

• Part A Find the likelihood function associated with the Poisson distribution
• Part B Using this, confirm that the MLE for the Poisson is

\[ \hat{\lambda} = \frac{1}{n} \sum_{i=1}^n x_i \]