How to Estimate the exponent a?

P=e^-aT in matlab?

[Jan]

"P~e^-aT where x is the size of the shield" - x does not occur in this equation. Later we find: "where T is the size of the shield".

[Walter Roberson]

Please do not close questions that have an answer.

Answer 1

[Jan]

You have the equation P ~ exp(-aT). You determine the value of P by the simulation and have T as input parameter. Then it seems to be trivial to solve this equation to obtain a:

a = -log(P) / T

Instead of collecting the results in a diagram only, you need to store the final positions in an array. E.g.:

% x_t(1) = 0;  % Remove this
% y_t(1) = 0;  % Remove this 
x_final = zeros(1, M);
y_final = zeros(1, M);
for m = 1:M
  x_t = zeros(1, N);
  x_t = zeros(1, N)
  for n = 1:N-1  % Not until N, but N-1!
      ...
  end
  x_final(m) = x_t(N);
  y_final(m) = y_t(N);
end

Now you can determine P by comparing the final positions with the goal.

[Jan]

While "A=++" is no valid Matlab syntax, I assume you need something like this:

P = sum(x_final > T) / M;
a = -log(P) / T

I do not understand, why you ask for "x(N+1)=x(N)+1". I showed you a way to store the final positions and the method to calculate the parameter a based on the results of the simulation. Keep the rest as you like.