DESCRIPTION Students: Please keep in mind the OMSI rules. Save your files often, make sure OMSI fills your entire screen at all times, etc. Remember that clicking CopyQtoA will copy the entire question box to the answer box. In questions involving code which will PARTIALLY be given to you in the question specs, you may need add new lines. There may not be information given as to where the lines should be inserted. If a question includes test code, make sure to include it in your submission. Do not answer any question with simulation code unless this is specified. MAKE SURE TO RUN THE CODE IN PROBLEMS INVOLVING CODE! Hit the OMSI Submit and Run button. QUESTION -ext .R -run 'Rscript omsi_answer1.R' (R code answer, 25 pts.) In the example on p.130, find P(X < 1.6). print( ) QUESTION -ext .R -run 'Rscript omsi_answer2.R' (R code answer, 25 pts.) In the example on p.33, let M be the number of kings drawn. Find F_M(2.2). print( ) QUESTION -ext .R -run 'Rscript omsi_answer3.R' (R code answer, 25 pts.) A vendor guarantees a certain product for 6 months. We treat the lifetime L in months of the product as a discrete random variable taking on the values 1,2,3,... If L <= 2, the vendor refunds the purchaser $5. If 2 < L <= 6, the vendor gives a refund of $1. Find the expected payout (per purchaser). Assume the lifetime of the product has a geometric distribution with p = 0.25, so that P(L = 3) = 0.75^2 0.25. print( ) QUESTION -ext .R -run 'Rscript omsi_answer4.R' (R code answer, 25 pts.) Write a function q(v) to compute the inverse of F_X on p.130, for 0 < v < 1. q <- function(v) { } print(q(0.36))