We are given the following square dartboard with side length = 2 units, with a circle of radius 1 unit inscribed in it and a certain region shaded red (namely, the bottom half of the square + the upper semi-circle, as shown in the picture). Suppose we throw 1000 darts on the given square dartboard and 892 of them land in the red area. Use this information to estimate π.                                                         

Which high-level simulation modeling approach does ARENA employ?

Which of the following statements about ARENA is incorrect?

Consider the following event list for a FIFO single-server queue, where is the customer’s sequence number, is the customer’s interarrival time, is the customer’s arrival time, is the customer’s service start time, and is the customer’s service time. Event list for FIFO What is the average waiting time for the customers in the queue?  

On a particular river, overflow floods occur once every year on average. Calculate the probability of 2 overflow floods in a particular year. Assume the number of floods follows a Poisson distribution.

Which of the following statements about the future events list (FEL) is TRUE?

Suppose that is a random variable with a mean of 6 and variance of 9, is a random variable with a mean of −10 and variance of 4, and = 2 . Find .

Let and  be two random variables such that . Assume their joint probability density function is given by:

Suppose that  and are i.i.d. random variables. How would you simulate a discrete uniform random integer between 1 and 12 (e.g., a 12-sided die toss)? 

Consider the discrete random variable :