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mean) you would type ?mean to see the help file. Make sure that you read the documentation of the relevant R function carefully, because the distribution may not be defined in the R function the same way it is designed in our lecture notes. All answers must be correct in terms of the way the distribution is defined in the lecture notes. Note that you are not expected to do the question by hand; no marks will be awarded for this. You need to provide the R code that computes the answer, together with the R output. Total Marks: 45 Questions Note that each student receives different questions! Make sure you answer your questions and not someone else's! 1. (4 marks) If X is a binomially distributed random variable with parameters n = 36 and p = 0.07, find Pr(X 2 4) and Pr(X = 8). 2. /4 marks) If X is a geometrically distributed random variable with parameter p = 0.09, find Pr(X 11) and the value of q such that Pr(X q) = 0.52. 9. /4 marks) If X is a Gamma-distributed random variable with parameters o = 4.3 and B = 1.5, find Pr(X > 1.1) and the value of q such that Pr(X -1.07) and the value of q such that Pr(X 0.13nY > -2.18) and the value of q such that Pr(X > qnY > q) =0.8. Hint: install the R package called mvtnorm