statistics-math

# Statistics & Mathematics Mathematical foundations for data science, machine learning, and statistical analysis. ## Quick Start ```python import numpy as np import scipy.stats as stats from sklearn.linear_model import LinearRegression # Descriptive Statistics data = np.array([23, 45, 67, 32, 45, 67, 89, 12, 34, 56]) print(f"Mean: {np.mean(data):.2f}") print(f"Median: {np.median(data):.2f}") print(f"Std Dev: {np.std(data, ddof=1):.2f}") print(f"IQR: {np.percentile(data, 75) - np.percentile(data, 25):.2f}") # Hypothesis Testing sample_a = [23, 45, 67, 32, 45] sample_b = [56, 78, 45, 67, 89] t_stat, p_value = stats.ttest_ind(sample_a, sample_b) print(f"T-statistic: {t_stat:.4f}, p-value: {p_value:.4f}") if p_value < 0.05: print("Reject null hypothesis: significant difference") else: print("Fail to reject null hypothesis") ``` ## Core Concepts ### 1. Probability Distributions ```python import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt # Normal Distribution mu, sigma = 100, 15 normal_dist = stats.norm(loc=mu, scale=sigma) x = np.linspace(50, 150, 100) # PDF, CDF calculations print(f"P(X < 85): {normal_dist.cdf(85):.4f}") print(f"P(X > 115): {1 - normal_dist.cdf(115):.4f}") print(f"95th percentile: {normal_dist.ppf(0.95):.2f}") # Binomial Distribution (discrete) n, p = 100, 0.3 binom_dist = stats.binom(n=n, p=p) print(f"P(X = 30): {binom_dist.pmf(30):.4f}") print(f"P(X <= 30): {binom_dist.cdf(30):.4f}") # Poisson Distribution (even...