Question

A random walk is a stochastic process in which a particle moves one step at a time from state to state in a structured space. For us, the state space will be Z, the set of integers. The particle starts in an initial state S[0] ∈ Z. If, after i ≥ 0 steps, the particle is in state S[i], then in step i + 1, it moves to state S[i] + 1 with probability p and to state S[i] − 1 with probability q; it cannot stand still. Of course, p + q = 1. If S[0] = 5 and 0 < p < 1, then the sequence 5,4,3,4,3,2,3,2,3,4 is a possible sequence of states for the particle if it moves 9 times.

Write a program that will simulate a random walk for a given number of steps and that will compute certain statistics for the random walk. The parameters for a simulation come from standard input as a single line of parameters, consisting of (1) the initial state S[0]; (2) the value of p; and (3) the number of steps to simulate.

Note: I’m writing this in Java.
So far I have:

public static void main(String[] args) {

    Random rand = new Random();
    int iState = rand.nextInt();
    int particle = iState;
    double pValue = 0.60;
    int numSteps = rand.nextInt() + 1;
    int nSteps = 0;

    if (numSteps>=0) {
        System.out.println(particle);
        while (nSteps<numSteps); {

            if (rand.nextDouble() < pValue)
                particle++;

            else
                particle--;

            System.out.println(particle);
            nSteps++;

        }

    }

Something seems to be going wrong though, so I’m stuck.

EDIT: Thanks guys, somehow I didn’t catch that semicolon.

//—————————————————————————————-

EDIT 2: Okay, so I have the code working correctly; however, in the end I am supposed to listed the maximum, minimum, and average values. Is this possible to do without creating a new variable for each iState value? My new code is

 public static void main(String[] args) {

    Random rand = new Random();
    int iState = rand.nextInt();
    double pValue = 0.60;
    int numSteps = rand.nextInt(100) + 1;
    int nSteps = 0;

    if (numSteps>=0) {
        System.out.println(iState);
        while (nSteps<numSteps) {

            if (rand.nextDouble() < pValue)
                iState++;

            else
                iState--;

            System.out.println(iState);
            nSteps++;

Answer 1

I think your problem is that you need to delete the semicolon in the line

while (nSteps<numSteps); {

Also, you almost certainly don’t want to iterate for rand.nextInt() + 1 steps, since rand.nextInt() could be negative. You might mean rand.nextInt(n) where n is some upper bound, though, or you might just set it to n.

UPDATE: If you need to track the minimum, maximum, and average values, you might do something like

 int min = iState; // initial value
 int max = iState; // initial value
 long total = iState; // initial value

Then, after each iteration, you say

 min = Math.min(min, iState);
 max = Math.max(max, iState);
 total += iState;

and then at the end of the iteration, your minimum is in min, your maximum is in max, and your average is (double) total / numSteps.