a) We have a Linear Congruential Generator ( LCG ) with, a=4,c=3,m=10 and Z0=7. i. What is the period of the generator? ii. Is this a full period LCG? Briefly explain your answer. iii. Is this a good LCG? Explain your answer. b) Which of the following variables could be modeled with a discrete distribution and which with a continuous one? i. Inter-arrival times for customers in a bank. ii. The number of arrivals of patients in a hospital during, one hour. iii. The throughput of a production line that produces gears.| iv. The number of items inspected before encountering the first defective item. v. The time that a customer of a restaurant needs to decide for his order. vi. For a machine, whose time between failures follows the exponential distribution, the number of the failures that it gets in a year. vii. Number of "defective" items in a batch of size t. c) Let's say that you want to simulate the processing time of a machine and you have no historical data or designer estimates. You ask the operator of the machine, and you get this response: "Most of the times the machine needs about 2 minutes to process a part. Moreover, the processing time is never below 1 minute and never above 5 minutes". According to this information, which distribution would you select and what values would you give to its attributes?Justify your answer. d) We use the mid-square method to create random numbers. Our first number Z0is7012. Calculate the first 5 random numbers that the method will create