Homework: Monte Carlo Estimation

In preparation for the lab, carefully review the code below and answer these questions.

1. What does this program do?
2. What is the program output if the user enters 10000 when prompted for the number of points?
3. How would your answer to the above question change if the test in line 15 used <= rather than <?
4. Print the homework or copy and paste the code below in your homework. Draw a box around each statement, and underline each expression, in the code. (Even though technically an assignment in Java is an expression, do not underline entire assignments.)

The Random component provides a pseudo-random number generator that generates numbers uniformly distributed in the `[0.0,1.0)` interval; the method call rnd.nextDouble() returns a pseudo-random number in the `[0.0,1.0)` interval. (In case you're not familiar with the notation here, `[0.0,1.0)` denotes an interval consisting of all real numbers between 0.0 inclusive and 1.0 exclusive, i.e., the set of all values `x` satisfying `0.0 ≤ x < 1.0`.)

public static void main(String[] args) {
    SimpleReader input = new SimpleReader1L();
    SimpleWriter output = new SimpleWriter1L();

    output.print("Number of points: ");
    int n = input.nextInteger();

    int ptsInInterval = 0, ptsInSubinterval = 0;

    Random rnd = new Random1L();

    while (ptsInInterval < n) {
        double x = rnd.nextDouble();
        ptsInInterval++;
        if (x < 0.5) {
            ptsInSubinterval++;
        }
    }

    double estimate = (100.0 * ptsInSubinterval) / ptsInInterval;
    output.println("Estimate of percentage: " + estimate + "%");

    input.close();
    output.close();
}