A sonnet is a 14-line poem in which certain rhyming patterns are followed. The writer Raymond Queneau published a book containing just 10 sonnets, each on a different page. However, these were structured such that other sonnets could be created as follows: the first line of a sonnet could come from the first line on any of the 10 pages, the second line could come from the second line on any of the 10 pages, and so on (successive lines were perforated for this purpose) (a) Create a function in R called remove_pages that receives a positive integer i and returns the probability that none of the lines from the sonnet created comes from the first i pages. Round the probabilities to 4 decimal places. (Hint: First write a mathematical formula to compute this that depends on i you already did this for i = 2- and then write this in R, make sure you use parentheses for powers like 10 (14), etc.) (b) Create an empty vector called probs.sonnet with 10 entries. Then, with a for loop, store remove-pages(i) in the i-th slot of probs. sonnet, where i = 1,...,10. A sonnet is a 14-line poem in which certain rhyming patterns are followed. The writer Raymond Queneau published a book containing just 10 sonnets, each on a different page. However, these were structured such that other sonnets could be created as follows: the first line of a sonnet could come from the first line on any of the 10 pages, the second line could come from the second line on any of the 10 pages, and so on (successive lines were perforated for this purpose) (a) Create a function in R called remove_pages that receives a positive integer i and returns the probability that none of the lines from the sonnet created comes from the first i pages. Round the probabilities to 4 decimal places. (Hint: First write a mathematical formula to compute this that depends on i you already did this for i = 2- and then write this in R, make sure you use parentheses for powers like 10 (14), etc.) (b) Create an empty vector called probs.sonnet with 10 entries. Then, with a for loop, store remove-pages(i) in the i-th slot of probs. sonnet, where i = 1,...,10