[Probability and Statistics] Binomial distribution simulation using statistically independent Bernoulli trials in Python.
Homework/project in Probability and Statistics (13E082VISR) at the University of Belgrade, School of Electrical Engineering.
Function BernoullisTrials(n, p, N) executes N independent simulations. Each simulation consists of n Bernoulli's experiments - n random numbers from interval [0,1] are generated and compared with the given probability of success p. The function returns a vector of length n+1 containing relative frequencies of possible number of successful experiments during the simulation.
def BernoullisTrials(n, p, N):
f = np.zeros(n + 1)
for simulation in range(0, N):
countSuccessfulTrials = 0
for trial in range(0, n):
if np.random.rand() < p:
countSuccessfulTrials += 1
f[countSuccessfulTrials] += 1
return f / N
The histogram shows relative frequencies obtained by simulating Bernoulli experiments (blue) and the actual binomial distribution probabilities (orange).
The simulation is repeated four times for various number of iterations (100 and 1000), and root-mean-square error is calculated for each simulation to compare the results with theoretical binomial distribution frequencies.
| Simulation | RMSE (N=100) | RMSE (N=1000) |
|---|---|---|
| No. 1 | 0.02404 | 0.00645 |
| No. 2 | 0.02109 | 0.00639 |
| No. 3 | 0.01871 | 0.00914 |
| No. 4 | 0.02452 | 0.00823 |