Programming question

[Pat]

I am a C++ beginner, please give me some suggestion on the following
question.

Given n balls. The probability pi is the chance to choose ball i. Sum of pi
is 1.

I want to run 10000 independent trials in selecting the ball, and simulate
the expected number of each ball to be choosen.

I have no idea how to implement the probability drawing step. Could you give
me some hints?
Thanks.

Pat

 

[Daniel T.]

I am a C++ beginner, please give me some suggestion on the following
question.

Given n balls. The probability pi is the chance to choose ball i. Sum of pi
is 1.

I want to run 10000 independent trials in selecting the ball, and simulate
the expected number of each ball to be choosen.

I have no idea how to implement the probability drawing step. Could you give
me some hints?

Look up how to use the 'rand()' function.

 

[Victor Bazarov]

I am a C++ beginner, please give me some suggestion on the following
question.

Given n balls. The probability pi is the chance to choose ball i. Sum of pi
is 1.

I want to run 10000 independent trials in selecting the ball, and simulate
the expected number of each ball to be choosen.

I have no idea how to implement the probability drawing step. Could you give
me some hints?

This is not really a C++ language question, and as such it doesn't belong
here, in all honesty. Please ask generic programming questions in
comp.programming and generic mathematics questions in sci.math.

Some hints: usually simulating with a computer something that occurs at
random requires the use of pseudo-random number generator. There is one
in the Standard C++ library. Its interface consists of two functions
named 'rand' and 'srand'. Since computers are pretty much deterministic
devices when it comes to programmed behaviour, simulating real-time random
situations with computers is tricky and requires some assumptions to be
made. You need to figure out what "10000 independent trials" really means
because if it's all in the same program, it's not really _independent_.

Victor

 

[Stuart McGarrity]

It would probably be quicker to design the algorithm in something like
MATLAB first (in this case 10 min) then look at implementing it in C++ once
you know what your doing if you need to.

One algorithm is:

% Generate probabilities
n=100; % Number of balls
trials=100000; % Number of independant trials
pi=rand(n,1); % n different probabilities of a ball being choosen
pi=pi/sum(pi); % Ensure sum is 1
cumpi=cumsum(pi); % Cumulative sum of probabilities

%% Simulate
count=zeros(n,1); % Set all ball counts to 0
for i = 1:trials
pick=rand; % Pick a number between 0 and 1
choosen=sum(cumpi<pick)+1; % Find which ball this corresponds too
count(choosen)=count(choosen)+1; % Count ball
end

Stuart

 

[Kai-Uwe Bux]

I am a C++ beginner, please give me some suggestion on the following
question.

Given n balls. The probability pi is the chance to choose ball i. Sum of
pi is 1.

I want to run 10000 independent trials in selecting the ball, and simulate
the expected number of each ball to be choosen.

I have no idea how to implement the probability drawing step. Could you
give me some hints?
Thanks.

Pat

a) This is off-topic here.
b) Google for "J.A. Walker's alias method" or look up

D.E. Knuth
The Art of Computer Programming Vol 2,
page 120--121

for a description.


Best

Kai-Uwe Bux