指数分布

def solve():
    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats
    mean_time = 10
    prob_5min = stats.expon.cdf(5, scale=mean_time)
    print(f"5分钟内到达的概率: {prob_5min:.4f}")
    x = np.linspace(0, 40, 1000)
    pdf = stats.expon.pdf(x, scale=mean_time)
    plt.figure(figsize=(10, 6))
    plt.plot(x, pdf, 'b-', linewidth=2)
    plt.fill_between(x[x<=5], pdf[x<=5], alpha=0.3, color='red', label=f'P(X≤5)={prob_5min:.4f}')
    plt.xlabel('时间 (分钟)')
    plt.ylabel('概率密度')
    plt.title('指数分布')
    plt.legend()
    plt.grid(alpha=0.3)
    plt.show()