Generate A Sequence of 25 Independent Bernoulli RVs with p = .8?

I have a question that asks me to generate a sequence of 25 independent Bernoulli RVs where p = .8. I want to see how many random numbers are needed to achieve this.

Here's what I have gathered so far ...

X = rand(1); Y = ( X <= p ); % Will generate Y = 0 if false, Y = 1 if true.

I want to create a vector with all of the Y values of 0s and 1s and have the program terminate after 25 1's have been generated. Then I want to find out the length of the entire vector with 0's and 1's.

Any help you can provide me would be GREATLY appreciated!

Answer 1

[SK]

If you are not too concerned about efficiency, and I suspect that you are not, you could use a while loop.

p = 0.8;
Y(35,1) = false; % Create a column vector of 35 zeros
ones_count = 0;
i = 1;
while (ones_count < 25)
  Y(i) = (rand <= p);
  ones_count = ones_count + Y(i);
  i = i + 1;
end
Y(i : end) = []; % Clear unused part of vector. A misleadingly simple operation.
number_of_rands = length(Y);

Of course, the initial allocation of 35 elements for Y may not be sufficient, but that is unlikely. Even if not sufficient, Matlab will create the new elements for you, albeit inefficiently, when you do Y(i) = ... for i > 35. In any case writing:

Y(i:end) = [];

Makes your code inefficient, so no point worrying about efficiency.

[Steven]

Thank you so much! This makes sense!