using matlab's arrayfun(), run a monte-carlo simulation with 100'000 replications to approximate the probability of . in matlab

To use arrayfun() to run a Monte-Carlo simulation of 100,000 replications and compute the probability of an event, you can follow these steps:

1. Define a function to perform one replication of the simulation and return 1 if the event occurs, and 0 otherwise.

main.m
function result = one_replication()
    % Compute the result of one replication here
    if (event_occurs)
        result = 1;
    else
        result = 0;
    end
end
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2. Use arrayfun() to call this function 100,000 times and store the results in a vector.

main.m
results = arrayfun(@(x) one_replication(), 1:100000);
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The @(x) syntax creates an anonymous function that calls one_replication() for each value of x in the range 1 to 100,000.

3. Compute the probability of the event by taking the mean of the results vector.

main.m
probability = mean(results);
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Since each element of results is either 0 or 1, the mean of the vector gives the proportion of times the event occurred, which is an estimate of the true probability.

Note that you will need to replace the comment in the one_replication() function with the actual simulation code.