Binomial Distribution [Miller and Freund] Matlab [ Martinez 2001]

Repeated trials with getting x successes in n trials i.e, x successes and n-x failures in n attempts.
Assumption involves:

1. Only 2 possible outcomes for each trial: success and failure
2. The probability of success is the same for each trial
3. There are n trials, where n is constant
4. The n trial are independent

Trials satisfying this assumptions are reffered to as Bernoulli random variables.

for x = 0, 1, 2, ... , n

Expected Value (mean) E[X]= np ; Variance V(x) = np(1-p)
discriptions:

n : trials
x : successes
n - x : failures
p : probability of success
1-p : probability of failure
| n|
| x| : called binomial coefficient , which is the no of combination of x objects selected from a set of n object = n! / (r!(n-r)!)

MATLAB EXAMPLE on Binomial distribution using both probability mass function and cummulative distribution function.