Rand with product less than value

The number of iterations it takes for the product of two random numbers to produce a number less than 1e-5.

Attempt at solution:

    while 2
    %     randomIntegers < 1e-05
        count1 = count1 +1;
        randomIntegers = randi([-10,10],[20,1]);

        if randomIntergars > 1e-05
            break
        end

    end

EDIT: SECOND ATTEMPT

    while z < 1e-05
        count1 = count1 + 1;
        c = rand(1,1); %rand 1x1 matrix
        z = floor(c + (b-c+1) * rand(b,1));
        if c > 1e-05
            break
        end

    end

Nothing working no idea why?

[Walter Roberson]

Please describe the result that you expected

randi([-10,10],[20,1])

to have ?

[Steven]

Generate 20 random numbers between -10 to 10

[Steven]

% while z < 1e-05
%     count1 = count + 1;
%     x = rand(1,1); %rand 1x1 matrix
%     z = floor(a + (b-a+1) .* rand(b,1));
%     if z < 1e-05
%         break
%     end
%     
% end

I tried this but this doesn't work either

[Walter Roberson]

Please do not close Questions that have an Answer

Answer 1

[Star Strider]

This works when I tried it:

rndprd = 1;
k1 = 1;
while rndprd > 1E-5
    a = rand;
    b = rand;
    rndprd = a*b;
    k1 = k1 + 1;
end

fprintf(1,'\n\tRequired %d iterations to produce a product of random numbers (%.6f x %.6f) = %13.5E\n\n',k1, a, b, rndprd)

EDIT — Changed fprintf statement.

[Steven]

Oh right, I wasn't generating two random numbers that was my problem.

Thanks I think that works

[Star Strider]

My pleasure.

Answer 2

[Walter Roberson]

randi() generates random integers. You are generating 20 random integers, not 20 random numbers.

Then you have

if randomIntergars > 1e-05

The randomIntergars > 1e-05 tests whether each of the 20 integers is greater than 1e-05, creating a vector of 20 true and false values. When you apply "if" to a vector of logical values, the result is considered "true" only if all of the entries are true. There are 21 possible integer values in -10 to +10, of which 10 are greater than 1e-5. If the random number generator is "fair", then the probability that all of the entries will be greater than 1e-5 is then (10/21)^20 which is roughly 3.6*10^(-7). It will probably happen eventually, but it might take rather some time -- on average roughly 2.8 * 10^6 trials.

Now, when you do eventually find a list of 20 random numbers from the range with all of them greater than 1e-5, then since the minimum value for each of them will be 1, you can be sure that the minimum value of the product of any 2 or more of them will be 1. But your question is asking about the number of iterations to find a product less than 1e-5.

When you are working with integers, the product of any subset of them is going to be an integer, so the question of whether the product is less than 1e-5 is going to be the same as the question of whether the product is less than or equal to 0. The product of integers is 0 if any of the integers are 0, and otherwise the product is less than 0 if an odd number of the integers is less than 0. For example -9 * +8 = -72 and -72 < 1e-5.

However.. the question asks about the product of "two random numbers". There is nothing there to indicate that the random numbers were to be confined to the integers in -10 to +10, and there is nothing there to indicate that a uniform random distribution is to be used. Perhaps a Normal distribution should be used. Perhaps a Poisson distribution should be used. Perhaps a sum of a negative exponential and a Beta distribution should be used. Your question gives us no way to know.