(pi\\) appears in the formula for the standard normal distribution, the most important probability distribution in statistics. Why not give it a try to calculate \\(\\pi\\) using statistics! In fact, you'll use a simulation technique called the Monte Carlo Method. Recall that the area of a circle of radius \\(r\\) is (A = pir 2\\). Therefore the area of a circle of radius 1, aka a unit circle, is \\(pi\\). You'll compute an approximation to the area of this circle using the Monte Carlo Method. a. [5 Pts] The Monte Carlo Method uses random numbers to simulate some process. Here the process is throwing darts at a square. Assume the darts are uniformly distributed over the square. Imagine a unit circle enclosed by a square whose sides are of length 2. Set an R variable area. square to be the area of a square whose sides are of length 2. #INSERT YOUR ANSWER HERE b. [> Pts] The points of the square can be given x-y coordinates. Let both x and y range from -1 to +1 so that the square is centred on the origin of the coordinate system. Throw some darts at the square by generating random numeric vectors x and y, each of length N = 10,000. Set R variables x and y each to be uniformly distributed random numbers in the range -1 to +1. (hint: runif() generates random number for the uniform distribution) #INSERT YOUR ANSWER HERE c. [10 Pts] Now count how many darts landed inside the unit circle. Recall that a point is inside the unit circle when \\(x 2 + y 2