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Binomial
Distribution

When a
binomial
distribution of events is being considered, we can use
this algorithm to calculate the probability of obtaining a given number
of successes in a given number of Bernoulli
trials. It is necessary to provide the probability of
succes on a single trial.
We don't
use any special statistical toolbox or function here. 
where
N
= the number of trials
n
= the exact number of successes
p
= the probability of success
First, we can clear the current Matlab workspace and also the screen,
to keep things clean...
clear;
clc;
Then, we ask the user to enter the three required numbers... We use the
'input'
function in Matlab for this purpose,
n
=
input('Number of trials: ');
x
=
input('Exact number of successes: ');
p
=
input('Probability of success: ');
Now, this is the main algorithm to solve the problem,
m1
=
log(factorial(n));
m2
=
log(factorial(x));
m3
=
log(factorial(nx));
r
=
exp(m1  m2  m3 + x*log(p) + (nx)*log(1p));
Finally, we display the answer (the instruction 'num2str' transforms
a number into a string),
str
=
['Probability of ' num2str(x) ' successes in ' ...
num2str(n)
' trials: ' num2str(r)];
disp(str)
See the example
running...
What is the
probability of getting three heads in five tosses of a fair coin?
Number of trials: 5
Exact number of successes: 3
Probability of success: .5
And the Matlab response is
Probability of 3 successes in 5 trials: 0.3125
What is the
probability that in five rolls of a fair die, a number 1 appears twice?
Number of trials: 5
Exact number of successes: 2
Probability of success: 1/6
And the response is
Probability of 2 successes in 5 trials: 0.16075
Reference:
Poole, L.; Borchers, M.; Some Common Basic Programs;
Osborne/McGrawHill;
3rd. edition; Berkeley, CA; 1979.
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