Practical Exercises for Chapter 11
Ah, the moment you've all been waiting for—the practical exercises! We promise, the hands-on work is not just immensely educational but also lots of fun. These exercises will help you grasp the concept of probability and the Bayesian Theory more deeply. Let's jump in!
Exercise 1: Roll the Die
Simulate the roll of a fair six-sided die 1,000 times. Plot a histogram to show the distribution of the results.
import matplotlib.pyplot as plt
import random
results = [random.randint(1, 6) for _ in range(1000)]
plt.hist(results, bins=6, edgecolor='black')
plt.xlabel('Die Face')
plt.ylabel('Frequency')
plt.title('Frequency Distribution of 1,000 Die Rolls')
plt.show()
Exercise 2: Bayesian Inference for a Coin Toss
You have a biased coin that lands heads 60% of the time. If the coin is tossed 10 times, what is the probability that it lands heads exactly 7 times?
You can use the binomial probability...