Directions: Please submit a copy of your brief answers and description as well as your R code (in txt file) with a description for the functions using (# the comment command in R). Please submit the homework before 11:59 PM. 1. The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the other two doors, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Conduct a simulation study where you will find the probability of winning if you switch the door. Note: Present the simulation study in a functional format where you can choose the total number of trials (n). Clearly describe the steps of the algorithm. The final outcome of the study will be the estimated probability of winning the car, computed as p = (#number of times you won the car). Directions: Please submit a copy of your brief answers and description as well as your R code (in txt file) with a description for the functions using (# the comment command in R). Please submit the homework before 11:59 PM. 1. The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the other two doors, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Conduct a simulation study where you will find the probability of winning if you switch the door. Note: Present the simulation study in a functional format where you can choose the total number of trials (n). Clearly describe the steps of the algorithm. The final outcome of the study will be the estimated probability of winning the car, computed as p = (#number of times you won the car)
