Recall the coupon collector problem discussed in class which has many applications in computer science. Consider a bag that contains N different types of coupons (say coupons numbered 1 . . . N). There are infinite number of each type of coupon. Each time a coupon is drawn from the bag, it is independent of the previous selection and equally likely to be any of the N types. Since there is an infinite number of each type, one can view this as sampling with replacement. Let T correspond to the random variable that denotes the number of total coupons that needed to be collected in order to obtain a complete set of at least one of each type of coupon. Write a R simulation code to estimate E(T) considering the following: • N denotes the total number of coupons. Run your numerical simulation to develop an estimate of E(T) and plot E(T) for N = 10, 20,30,40,50,60. (Use 1000 trials or more, i. e, Nsim > 1000).
• We showed in class that for large N, E(T) can be approximated by N log(N) +0.577N +0.5. In the same plot show the theoretical value and summarize your observation regarding the accuracy of the approximation.

a  social news website  is an  internet  website  that features  user-posted stories. such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. users typically comment online on the news posts and these comments may also be ranked in popularity. since their emergence with the birth of  web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. all such websites allow the users to submit content and each site differs in how the content is moderated. on the  slashdot  and  fark  websites,  administrators  decide which articles are selected for the front page. on  reddit  and  digg, the articles that get the most votes from the community of users will make it to the front page. many social news websites also feature an online comment system, where users discuss the issues raised in an article. some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. some social news websites also have a  social networking  function, in that users can set up a user profile and follow other users' online activity on the website.

a  social news website  is an  internet  website  that features  user-posted stories. such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. users typically comment online on the news posts and these comments may also be ranked in popularity. since their emergence with the birth of  web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. all such websites allow the users to submit content and each site differs in how the content is moderated. on the  slashdot  and  fark  websites,  administrators  decide which articles are selected for the front page. on  reddit  and  digg, the articles that get the most votes from the community of users will make it to the front page. many social news websites also feature an online comment system, where users discuss the issues raised in an article. some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. some social news websites also have a  social networking  function, in that users can set up a user profile and follow other users' online activity on the website.