# Importing the libraries we need
import warnings; warnings.filterwarnings("ignore")
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Data setup
df_titanic = sns.load_dataset("titanic")
print("Titanic shape:", df_titanic.shape)
print(df_titanic.head())

# Bernoulli Distribution: Simulating one coin flip
p = 0.5  # Probability of heads
flip = np.random.binomial(1, p)
print(f"Coin flip result (1=heads, 0=tails): {flip}")

# Simulate 20 coin flips and plot the results
flips = np.random.binomial(1, p, 20)
print("Coin flip outcomes:", flips)
plt.figure(figsize=(5,2))
sns.histplot(flips, bins=2, discrete=True)
plt.xticks([0,1], ['Tails', 'Heads'])
plt.title('Coin Flip Outcomes: 20 Bernoulli Trials')
plt.ylabel('Count')
plt.show()

# Simulate 10 coin flips and count heads (k successes in n trials)
n = 10  # number of flips
p = 0.5  # probability of heads
heads_count = np.random.binomial(n, p)
print(f"Number of heads in 10 flips: {heads_count}")

# What does the binomial distribution look like?
results = [np.random.binomial(n, p) for _ in range(1000)]
plt.figure(figsize=(6,3))
sns.histplot(results, bins=n+1, discrete=True)
plt.xlabel('Number of Heads in 10 Flips')
plt.ylabel('Frequency')
plt.title('Distribution of Heads (10 flips, 1000 simulations)')
plt.show()

# Estimate probability: How often do we get at least 8 heads in 10 flips?
results = np.random.binomial(n, p, 10000)
prob_8_or_more = np.mean(results >= 8)
print(f"Probability of getting 8 or more heads in 10 flips: {prob_8_or_more:.3f}")

# Apply binomial idea to Titanic survivor data
n_total = df_titanic["survived"].dropna().shape[0]
p_survive = df_titanic["survived"].mean()
simulated_survivors = np.random.binomial(n_total, p_survive)
print(f"Out of {n_total} passengers, about {simulated_survivors} would survive with this probability.")

# Simulate how many emails you get in a day (lambda is average rate)
lam = 5  # average 5 emails per day
emails_per_day = np.random.poisson(lam)
print(f"You got {emails_per_day} emails today.")

# Simulate and plot your email counts for 30 days
emails = np.random.poisson(lam, 30)
plt.figure(figsize=(6,3))
plt.bar(range(1, 31), emails, color='skyblue')
plt.xlabel('Day')
plt.ylabel('Emails Received')
plt.title('Simulated Daily Email Counts for One Month')
plt.show()

# What most likely number of emails can you get in a day?
emails_samples = np.random.poisson(lam, 10000)
values, counts = np.unique(emails_samples, return_counts=True)
most_likely = values[np.argmax(counts)]
print(f"The most likely number of emails in a day is: {most_likely}")

# Input: Your estimated average emails per day
user_lambda = int(input("Estimate how many emails you get per day, on average: "))
sim = np.random.poisson(user_lambda, 14)
print(f"Emails you might get over 2 weeks: {sim}")

# Mini-project: Model rare phone calls per hour with Poisson
lam = 2  # average phone calls per hour
n_hours = 100
calls = np.random.poisson(lam, n_hours)
plt.figure(figsize=(6,3))
sns.histplot(calls, bins=range(0, max(calls)+2), discrete=True, color='coral')
plt.xlabel('Calls in an Hour')
plt.ylabel('Number of Hours')
plt.title('Simulated Phone Calls over 100 Hours')
plt.show()