You are interested in studying the writing style of a popular Time Magazine contributor, FZ. You collect a simple random sample of his articles and count how many times he uses the word "however" in each of the articles in your sample, (x1,,xn). In this set-up, xi is the number of times the word "however" appeared in the i-th article and let Xi denote the quantity that captures the number of times the word "however" appears in the i-th article.

Let's assume that the quantities X1,,Xn are independent and identically distributed (IID) according to a Poisson distribution with unknown parameter ,

p(Xi=xi) = Poisson(xi) for i=1,,n

• Write the log-likelihood l() for a generic sample of n articles, (x1,,xn).
• Write the log-likelihood l() for the following specific sample of 7 articles (12, 4, 5, 3, 7, 5, 6).
• Plot the log-likelihood l() in R for the same specific sample of 7 articles (12, 4, 5, 3, 7, 5, 6). What is the maximum value of (approximately)?