birthday problem: true simulation

The code below also contains code from the previous video, but it should give you the correct chart. Be mindful that the simulation might take a bit.

import pandas as pd

df = pd.read_csv("birthdays.csv")

plot_df = (df
  .assign(date = lambda d: pd.to_datetime(d['date']))
  .assign(day_of_year = lambda d: d['date'].dt.dayofyear)
  .groupby('day_of_year')
  .agg(n_births=('births', 'sum'))
  .assign(p = lambda d: d['n_births']/d['n_births'].sum()))

def sim_real_once(room = 20):
    r = np.random.choice(probabilities.index, p=probabilities, size=room)
    return np.unique(r).shape[0] != room

def simulate_real(room = 20, n_sim = 1000):
    return np.mean([sim_real_once(room) for _ in range(n_sim)])

plt.plot([calculate(r) for r in range(1, 35)], label="calculated")
plt.plot([simulate_real(room = i, n_sim=10_000) for i in range(1, 35)], label="simulated_real")
plt.legend();