Evaluate the following using R simulations and provide R scripts for each – Question 1 Assume and . For each value of , and using 10,000 random samples of , find . Plot answer for versus . Question 2...

Hi
Each of the 4 questions in the attached document needs to be resolved experimentally (i.e. through simulation). Please support each solution with a separate, well commented R script.
All answers must be received by tomorrow, the 23 January 2021 1200hrs UK (London) time.
Thank you


Evaluate the following using R simulations and provide R scripts for each – Question 1 Assume and . For each value of , and using 10,000 random samples of , find . Plot answer for versus . Question 2 By generating 10,000 samples from random variable find the value of for which is maximum. Assume . Question 3 The number of customers attending a shop in has Poisson distribution with parameter . The time that each customer spends in the shop has Exponential distribution with parameter . Find the probability that while a particular customer is shopping, maximum other customer arrive. Use (any) and . Use 10,000 samples. Question 4 Assume that the lifetime of the lamps made by factory A follows an Exponential distribution with average of 24000 hours. Assume we have of these lamps, and therefore the total time that we can use them would be equal to . The percentage of the time that we would use the first lamp is therefore presented as . For values of and using 10,000 random samples lamps, estimate the percentage defined above and plot the results verses