Getting the mean of when a random process hits a desired number of successes

Hi, I have an Nxn matrix, where usually N = 1000 and n = 20. I have written a code in order to make this matrix show me when the processes hits a certain number of successes, namely 10. Each line is one realization of the process. I need to pick the first time it hits 10, register in which trial it occurred, and then make a simple mean from the N lines of the matrix. (My code is attached to this question). Thanks in advance.

clear all;

N = 1000;
p = 0.4;
n = 20;

xn = rand(N,n);

% Tornando xr uma matriz de variavel indicadora

xn(xn >= 1-p) = 1;
xn(xn < 1-p) = 0;

% Tornando xr um processo estocastico Sa(n)

for i = 2:1:n
    xn(:,i) = xn(:,i) + xn(:,i-1);
end

xn(xn ~= 10) = 0;
xn(xn == 10) = 1;

This is what I was trying, it seemed to be working outside the for loop though,

contador = 0;

for i = 1:N
   contador = contador + find(xn(i,:),1);
end

mean = contador/N;

Answer 1

[Walter Roberson]

xn = cumsum( rand(N,n) >= 1-p, 2 ) == 10;
mean( arrayfun(@(K) find(xn(K,:),1), 1:N) )

But is it certain that 10 will be hit on every line?

[Philippe]

No, it is not certain. The xn matrix is a random process of an indicator random variable.

[Image Analyst]

And if there is no "10" in a row, then how do you want that to affect the mean? Just ignore it? Or something else?

[Philippe]

It doesn't seem to be working here yet.

[Philippe]

Good point, this is an exercise my professor gave me and his explanation of what to do was very confusing. I believe I would consider only the lines in which the process hits 10. Then my idea would be to get the column in which it hits 10 first, then make a simple mean with the sum of these columns divided by the number of lines in which the process hits 10.

[Image Analyst]

Well that's what I had but when I saw Walter had done the same thing as me for the first line, I deleted my answer. My second part does what you say but was more than 1 line and I assumed his worked. But now that we know it's your homework, we should not give you anymore or we'll have done 100% of it for you. That wouldn't be fair to your classmates, would it?

[Philippe]

Image Analyst, if you don't want to help feel free not to. My classmates and I are basically in the same situation: our professor gave us some vague coordinates and we are trying to do something with it. We like to learn so we help each other if it seems necessary.

[Walter Roberson]

My code does assume 10 will be hit on every line.

xn = xn(any(xn,2),:);

[Philippe]

Well, I was trying to be efficient by using the MATLAB style, but since that wasn't going anywhere, I made it with a more traditional programming. Here is what I came with:

indicador = 0;
N_indicador = 0;

for i = 1:N
    counter = 0;
    j = 1;
    while counter == 0 && j < 21
        if xn(i,j) == 1
            indicador = indicador + j;
            N_indicador = N_indicador + 1;
            counter = 1;
        else
            j = j + 1;
        end
    end
end

mean = indicador/N_indicador