Question about monte carlo simulation

I have a question about Monte Carlo Simulation.

Suppose that three random numbers are generated. a) Determine the probability that the numbers are in increasing order using a Monte Carlo simulation where (i) the distribution is uniform in [

[James Tursa]

What have you done so far? Do you know how to generate three random numbers? Do you know how to compare them to see if they are in increasing order? Do you know how to do this multiple times and count how many times they were in increasing order?

[John D'Errico]

You don't have a question. You DO have a homework problem. :) One on which you apparently have not started work, but should make an effort.

[Bo Wang]

I know how to generate random numbers, I just don't know what the probability is. Is the probability should be 1/factorial(n) or probability should be 1?

[Walter Roberson]

You appear to be missing a few characters from the end of your question. Part of what is missing is whether the distribution is over integers or over real numbers.

Answer 1

[James Tursa]

Monte Carlo means you will be estimating the probability by making a large number of sample runs (aka trials) and then counting. Suppose you have a loop that runs for 1000000 iterations. On each iteration you generate 3 random numbers and check to see if they are in increasing order. The estimated probability is then the number of times they were in increasing order divided by the total number of trials. E.g.,

n = 1000000;  % <-- The total number of trials
count = 0; % <-- A counter to keep track of the number of successes
for k=1:n
    % You put code here to generate your three random numbers
    if( numbers are in increasing order ) % <-- You fill in this logic
        count = count + 1;
    end
end
estimated_probability = count / n;

[Bo Wang]

this helps me a lot. Thank you!