https://stats.stackexchange.com/a/443918/69508

443918_69508.py

from scipy.stats import beta
import matplotlib.pyplot as plt
import numpy as np

params = (((8,2), (5,5), (2,8)), ((2,1), (1,1), (1,2)), ((0.8,0.2), (0.5,0.5), (0.2,0.8)))
title_suffixes = ('Bell-shape', 'Straight lines', 'U-shape')
colors = ('blue', 'yellow', 'red')

x = np.linspace(0, 1, 10000)

for i in range(3):
    fig, ax = plt.subplots(1, 1)
    ax.set_xlim(left=0, right=1)
    ax.set_ylim(bottom=0, top=4)
    ax.set_xlabel('X')
    ax.set_ylabel('Probability density')
    ax.set_title(f'PDF of Beta ({title_suffixes[i]})')
    for j, (a,b) in enumerate(params[i]):
        y = beta.pdf(x, a, b)
        ax.plot(x, y, color=colors[j])
        if i == 0:
            text_x = (a - 1) / (a + b - 2)
            text_y = beta.pdf(text_x, a, b) + 0.1
            text_x -= 0.05
        elif i == 1:
            text_x = 0.81
            text_y = beta.pdf(text_x, a, b) + 0.25
        else:
            text_x = x[np.argmin(y)] - 0.1
            text_y = np.min(y) + 0.1
        ax.text(text_x, text_y, s=f'Beta({a},{b})', color=colors[j])
    plt.show()